COORDINATE EQUATION PROBLEMS:

PROCESS 1 EXAMPLES:

a) Given the coordinate equation  7 = (x-5)² + (y+6)², change it to the form  0 = x² + y² + dx + ey + f .

b) Given the coordinate equation  18 = (x+3)² + (y-4)², change it to the form  0 = x² + y² + dx + ey + f .

Solution to a) : Solution to b):

PROCESS 1 SOLUTIONS:

PROCESS 2 EXAMPLES:

c) Given the centre (-4,7), and the radius √26, write the coordinate equation.

d) Given the centre (9,-2), and the radius √54, write the coordinate equation.

Solution to c) : Solution to d) :

PROCESS 2 SOLUTIONS:

PROCESS 3 EXAMPLE:

Given the centre (4,-9), and the point (10,-3), write the coordinate equation.

PROCESS 3 SOLUTION:

PROCESS 4 EXAMPLE:

Given the centre (7,12), and the area 21, write the coordinate equation.

PROCESS 4 SOLUTION:

PERPENDICULAR DISTANCE PROBLEMS:

PROCESS 1 EXAMPLE:

Given the point P(3,5) and the line 12x + 4y +3 = 0, find the perpendicular distance.

PROCESS 1 SOLUTION:

PROCESS 2 EXAMPLE:

Given the point P(2,5) and the line 3x + 5y = 8, find the perpendicular distance.

PROCESS 2 SOLUTION:

PROCESS 3 EXAMPLE:

Given the lines -4y + x + 9 = 0 and y - 5x = 12, find theperpendicular distance.

PROCESS 3 SOLUTION:

LINEAR EQUATION SYSTEM PROBLEM:

Solve by Graphing Example:

Given this system :

Solve graphically.  

y = x²y = 6 - x²

Solve by Graphing solution:

y = x²

  x | y   -1   1         --->         P(-1,1)  0   0         --->          P(0,0)  1  1         --->          P(1,1)  2   4         --->          P(2,4)  3   9         --->          P(3,9)  4   16       --->          P(4,16)  5   25       --->          P(5,25) 6   36       --->          P(6,36)

y = 6 - x² y = -x² + 6

  x | y   -1   5         --->        P(-1,5)  0   6         --->        P(0,6)  1  5         --->        P(1,5)  2   2         --->       P(2,2)  3   -3        --->        P(3,-3)  4   -10      --->        P(4,-10)  5   -19      --->        P(5,-19) 6   -30      --->        P(6,30)

(-1¾, 3) (1¾, 3)

The Solutions are (-1¾, 3) and (1¾, 3).

Solve by Substitution Example:

Given this system :

Solve using substitution.  

  12x - 4y = 9   y + 4x = 18

Solve by Substitution solution:

Solve by Elimination Example:

Given this system :

  4x + y = 30   -2x + 2y = 10

Solve using elimination.  

Solve by Elimination solution:

BIBLIOGRAPHY:

http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html