circles - vmkt.s3-ap-southeast-1.amazonaws.com

CIRCLES

CIRCLES

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y − 4 x + 3 = 0, then its radius is equal to :

A B C D2 1

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y − 4 x + 3 = 0, then its radius is equal to :

A B C D2 1

Solution :

11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics

A B C D6 13

A square is inscribed in the circle x2 + y2 - 6x + 8y - 103 = 0 with its sides parallel to coordinate axes.Then the distance between origin and vertex of this square which is nearest to the origin is

11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics

A square is inscribed in the circle x2 + y2 - 6x + 8y - 103 = 0 with its sides parallel to coordinate axes.Then the distance between origin and vertex of this square which is nearest to the origin is

A B C D6 13

11-01-2019 - Morning Shift - MathematicsSolution :

Equation of circle touching the lines |x - 2| + |y - 3| = 4 will be

A B

C D

(x - 2)2 + (y - 3)2 = 12 (x - 2)2 + (y - 3)2 = 4

(x - 2)2 + (y - 3)2 = 2 (x - 2)2 + (y - 3)2 = 8

Equation of circle touching the lines |x - 2| + |y - 3| = 4 will be

A B

C D

(x - 2)2 + (y - 3)2 = 12 (x - 2)2 + (y - 3)2 = 4

(x - 2)2 + (y - 3)2 = 2 (x - 2)2 + (y - 3)2 = 8

Solution :

x - y = 3

The equation of the image of the circle x2 + y2 + 16x - 24y + 183 =0 in the line mirror 4x + 7y + 13 = 0 is

A B

C D

x2 + y2 + 32x - 4y + 235 = 0 x2 + y2 + 32x + 4y - 235 = 0

x2 + y2 + 32x - 4y - 235 = 0 x2 + y2 + 32x + 4y + 235 = 0

The equation of the image of the circle x2 + y2 + 16x - 24y + 183 =0 in the line mirror 4x + 7y + 13 = 0 is

A B

C D

x2 + y2 + 32x - 4y + 235 = 0 x2 + y2 + 32x + 4y - 235 = 0

x2 + y2 + 32x - 4y - 235 = 0 x2 + y2 + 32x + 4y + 235 = 0

Solution :

09-01-2020-Morning Shift

A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle?

A B

C D

4x – 3y + 17 = 0 3x – 4y – 24 = 0

3x + 4y – 6 = 0 4x + 3y – 8 = 0

09-01-2020-Morning Shift

A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle ?

A B

C D

4x – 3y + 17 = 0 3x – 4y – 24 = 0

3x + 4y – 6 = 0 4x + 3y – 8 = 0

Solution :

12-04-2019-Evening Shift

A circle touching the X-axis at (3, 0) and making an intercept of length 8 on the Y-axis passes through the point :

A B C D(3, 10) (3, 5) (2, 3) (1, 5)

12-04-2019-Evening Shift

A circle touching the X-axis at (3, 0) and making an intercept of length 8 on the Y-axis passes through the point :

A B C D(3, 10) (3, 5) (2, 3) (1, 5)

Solution :

08-04-2019-Morning Shift

The sum of the squares of the lengths of the chords intercepted on the circle, x2 + y2 = 16, by the lines, x + y = n, n ∈ N, where N is the set of all natural numbers, is :

Solution :

The tangent to the circle C1 : x2 + y2 – 2x – 1 = 0 at the point

(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is ..

A B C D2 3

The tangent to the circle C1 : x2 + y2 – 2x – 1 = 0 at the point

(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is ..

The tangent to the circle C1 : x2 + y2 – 2x – 1 = 0 at the point

(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is :

A B C D2 3

Solution :

11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics

The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

A B C D

11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics

The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

A B C D

11-01-2019 - Morning Shift - MathematicsSolution :

08-01-2020-Evening Shift

If a line, y = mx + c is a tangent to the circle, ( x – 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point ; then

A B

C D

c2 + 7c + 6 = 0 c2 + 6c + 7 = 0

c2 – 6c + 7 = 0 c2 – 7c + 6 = 0

08-01-2020-Evening Shift

If a line, y = mx + c is a tangent to the circle, ( x – 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point ; then :

A B

C D

c2 + 7c + 6 = 0 c2 + 6c + 7 = 0

c2 – 6c + 7 = 0 c2 – 7c + 6 = 0

Solution :

08-04-2019-Evening Shift

The tangent and the normal lines at the point to the circle x2 + y2 = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :

A B C D

08-04-2019-Evening Shift

The tangent and the normal lines at the point to the circle x2 + y2 = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :

A B C D

Solution :

10-04-2019-Evening Shift

A B

C D

The locus of the centres of the circles, which touch the circle x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is:

10-04-2019-Evening Shift

The locus of the centres of the circles, which touch the circle x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is:

A B

C D

Solution :

The locus of the centre of a circle which touches externally the circle (x - 3)2 + (y - 3)2 = 4 and also touches the y-axis is given by the equation:

A B

C D

x2 - 6x - 10y + 14 = 0 x2 - 10x - 6y + 14 = 0

y2 - 6x - 10y + 14 = 0 y2 - 10x - 6y + 14 = 0

The locus of the centre of a circle which touches externally the circle (x - 3)2 + (y - 3)2 = 4 and also touches the y-axis is given by the equation:

A B

C D

x2 - 6x - 10y + 14 = 0 x2 - 10x - 6y + 14 = 0

y2 - 6x - 10y + 14 = 0 y2 - 10x - 6y + 14 = 0

Solution :

09-01-2020-Evening Shift

If the curves, x2 - 6x + y2 + 8 = 0 and x2 - 8y + y2 + 16 - k =0, (k > 0) touch each other at a point, then the largest value of k is

Solution :

09-01-2019-Evening Shift

If the circles x2 + y2 – l6x – 20y + 164 = r2 and (x – 4)2 + (y – 7)2 =36 intersect at two distinct points, then:

A B C Dr > 11 0 < r < 1 r = 11 1 < r < 11

09-01-2019-Evening Shift

If the circles x2 + y2 – l6x – 20y + 164 = r2 and (x – 4)2 + (y – 7)2 =36 intersect at two distinct points, then:

A B C Dr > 11 0 < r < 1 r = 11 1 < r < 11

Solution :

Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle when

A B

C D

All are integral values of K 0 < K < 1

K < 0 For two values of K

Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle when

A B

C D

All are integral values of K 0 < K < 1

K < 0 For two values of K

Solution :

If a circle passes through the points of intersection of the coordinate axes with the lines λx - y + 1 = 0 and x - 2y + 3 = 0, then the value of λ is

A B C D2 4 6 3

If a circle passes through the points of intersection of the coordinate axes with the lines λx - y + 1 = 0 and x - 2y + 3 = 0, then the value of λ is

A B C D2 4 6 3

Solution :

Leaderboard

Vaibhav Dubey Aditya Barkataky

Simran Abhay Srivastava

Teju Aquasa Aziz

Darshan Abhiraj Patil

Amit Raj Sinha Parth Bhatnagar

Aadish Jain Varun Gyanchandani

Pranjal Ambwani Shaharyar Ansari

Armaan Mittal Nitin Jha

Janvi Patel Reeti

Harshavardhan Pawar Aditya Ojha

Chirayu Jadhav Lakshay kumawat

Siddharth Goyal Juhi Juhi

Siddharth Tiwari Khushi Agarwal

Tatva Mohammed Abdulla

Niharika Choudhary

Leaderboard

The intercept on the line y = x by the circle x2 + y2 - 2x = 0 is AB. Equation of the circle with AB as a diameter is:

A B

C D

x2 + y2 + x + y = 0 x2 + y2 - x - y = 0

x2 + y2 + x - y = 0 None of these

The intercept on the line y = x by the circle x2 + y2 - 2x = 0 is AB. Equation of the circle with AB as a diameter is:

A B

C D

x2 + y2 + x + y = 0 x2 + y2 - x - y = 0

x2 + y2 + x - y = 0 None of these

Solution :

10-04-2019-Morning Shift

The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is:

A B C D3 2

10-04-2019-Morning Shift

The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is:

A B C D3 2

Solution :

12-01-2019 - Morning Shift12-01-2019-Morning Shift

Let C1 and C2 be centres of the circles x2 + y2 -2x - 2y – 2 = 0 and x2 + y2- 6x - 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles then, area (in sq. units) of the quadrilateral PC1QC2 is : ______

A B C D8 6 9 4

12-01-2019 - Morning Shift12-01-2019-Morning Shift

Let C1 and C2 be centres of the circles x2 + y2 -2x - 2y – 2 = 0 and x2 + y2- 6x - 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles then, area (in sq. units) of the quadrilateral PC1QC2 is : ______

A B C D8 6 9 4

12-01-2019 - Morning Shift

Solution :

10-04-2019-Morning Shift

If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for..

A

B

C

D

Infinitely many values of K

No value of K.

Exactly two values of K

Exactly one value of K

10-04-2019-Morning Shift

If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for..

10-04-2019-Morning Shift

If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for:

A

B

C

D

Infinitely many values of K

No value of K.

Exactly two values of K

Exactly one value of K

Solution :

07-01-2020-Evening Shift

Let the tangents drawn from the origin to the circle, x2 + y2 – 8x – 4y + 16 = 0 touch it at the point A and B. Then (AB)2 is equal to:

A B C D

07-01-2020-Evening Shift

Let the tangents drawn from the origin to the circle, x2 + y2 – 8x – 4y + 16 = 0 touch it at the point A and B. Then (AB)2 is equal to:

A B C D

Solution :

12-04-2019-Morning Shift

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :

A B C D

12-04-2019-Morning Shift

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :

A B C D

Solution :

From origin, chords are drawn to the circle x2 + y2 - 2y = 0. The locus of the middle points of these chords is

A B

C D

x2 + y2 - y = 0 x2 + y2 - x = 0

x2 + y2 - 2x = 0 x2 + y2 - x - y = 0

From origin, chords are drawn to the circle x2 + y2 - 2y = 0. The locus of the middle points of these chords is

A B

C D

x2 + y2 - y = 0 x2 + y2 - x = 0

x2 + y2 - 2x = 0 x2 + y2 - x - y = 0

Solution :

❖ Cover entire JEE Main Syllabus (as per the new pattern) with India’s Best Teachers in 90 Sessions

❖ Solve unlimited doubts with Doubt experts on our Doubt App from till Exam

8 AM to 11 PM

JEE MAIN 2021 CRASH COURSE

● 1 Batch Classes will be over in 10 Weeks

● 10 full and 10 Part syllabus test to make you exam ready

●● Amazing tricks & tips to crack JEE Main 2021

Questions in power-packed 90 Min sessions●● Learn on a 2-way Interactive Platform where

the teacher is always with you

JEE MAIN 2021 CRASH COURSE

Lightning Deal: ₹10000 ₹8000/-

Batch Starts From : Every Monday

*Crash Course Link Available in Description

Apply Coupon Code: AVKCC

Live Interactive Classes● LIVE & Interactive Teaching Style

● Fun Visualizations, Quizzes &

Leaderboards

● Daily Classes on patented WAVE platform

● Dual Teacher Model For Personal

Attention

Why Vedantu Pro is the Best?Test Series & Analysis

● Exclusive Tests To Enable Practical Application

● Mock & Subject Wise Tests, Previous Year Tests

● Result Analysis To Ensure Thorough Preparation

Assignments & Notes

● Regular Assignments To Ensure Progress

● Replays, Class Notes & Study Materials Available 24*7

● Important Textbook Solutions

● Full syllabus Structured Long Term Course

● 20+ Teachers with 5+ years of experience

● Tests & Assignments with 10,000+ questions

● Option to Learn in English or Hindi

● LIVE chapter wise course for revision

● 4000+ Hours of LIVE Online Teaching

● Crash Course and Test Series before Exam

What is Included in Vedantu Pro?

AVKPRO

2022

How to Avail The Vedantu Pro Subscription

*Vedantu Pro Subscription Link available in description

Use the code: AVKPRO

1Select Your

Grade & Target

Click on Get Subscription

2 3Apply Coupon Code and Make Payment

Choose Your Subscription & Click on Proceed To Pay

4

Join Vedantu JEE Telegram channel NOW!

https://vdnt.in/jeepro

Assignments

Daily Update

Notes