11X1 T12 07 chord of contact

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<ul><li><p>Chord of Contact</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ay</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ayWe know the coordinates of an external point (T)</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ay</p><p> 0 0,T x y</p><p>We know the coordinates of an external point (T)</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ay</p><p> 0 0,T x y</p><p>We know the coordinates of an external point (T)</p><p>From this external point, two tangents can be drawn meeting the parabola at P and Q.</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ay</p><p>2(2 , )Q aq aq</p><p>2(2 , )P ap ap</p><p> 0 0,T x y</p><p>We know the coordinates of an external point (T)</p><p>From this external point, two tangents can be drawn meeting the parabola at P and Q.</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ay</p><p>2(2 , )Q aq aq</p><p>2(2 , )P ap ap</p><p> 0 0,T x y</p><p>We know the coordinates of an external point (T)</p><p>From this external point, two tangents can be drawn meeting the parabola at P and Q.</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ay</p><p>2(2 , )Q aq aq</p><p>2(2 , )P ap ap</p><p> 0 0,T x y</p><p>We know the coordinates of an external point (T)</p><p>From this external point, two tangents can be drawn meeting the parabola at P and Q.The line joining these two points is called the chord of contact.</p></li><li><p>Chord of Contacty</p><p>x</p><p>2 4x ay</p><p>2(2 , )Q aq aq</p><p>2(2 , )P ap ap</p><p> 0 0,T x y</p><p>We know the coordinates of an external point (T)</p><p>From this external point, two tangents can be drawn meeting the parabola at P and Q.The line joining these two points is called the chord of contact.</p></li><li><p>(1) Parametric approach</p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq </p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p><p>3 Show that is the point ,T a p q apq</p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p><p>3 Show that is the point ,T a p q apq4 0 0But is ,T x y</p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p><p>3 Show that is the point ,T a p q apq4 0 0But is ,T x y </p><p>axqp</p><p>qpax</p><p>0</p><p>0</p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p><p>3 Show that is the point ,T a p q apq4 0 0But is ,T x y </p><p>axqp</p><p>qpax</p><p>0</p><p>0</p><p> apqy 0</p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p><p>3 Show that is the point ,T a p q apq4 0 0But is ,T x y </p><p>axqp</p><p>qpax</p><p>0</p><p>0</p><p>00 22 is yyaxxPQ </p><p>apqy 0</p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p><p>3 Show that is the point ,T a p q apq4 0 0But is ,T x y </p><p>axqp</p><p>qpax</p><p>0</p><p>0</p><p>00 22 is yyaxxPQ </p><p>Hence the chord of contact is yyaxx 00 2</p><p>apqy 0</p></li><li><p>(1) Parametric approach</p><p>1 Show that has equation 2 2PQ p q x y apq 2</p><p>2 2</p><p>Show the two tangents have equations0 and 0px y ap qx y aq </p><p>3 Show that is the point ,T a p q apq4 0 0But is ,T x y </p><p>axqp</p><p>qpax</p><p>0</p><p>0</p><p>00 22 is yyaxxPQ </p><p>Hence the chord of contact is yyaxx 00 2</p><p>apqy 0</p><p>notice similarity to tangent</p></li><li><p>(2) Cartesian approach</p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y </p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y T lies on PT 1010 2 yyaxx </p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y T lies on PT 1010 2 yyaxx </p><p> yyaxxyxP 0011 2equation with lineon the lies ,</p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y T lies on PT 1010 2 yyaxx </p><p>2 2 2Show that has equation 2QT xx a y y yyaxxyxP 0011 2equation with lineon the lies ,</p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y T lies on PT 1010 2 yyaxx </p><p>2 2 2Show that has equation 2QT xx a y y T lies on QT 2020 2 yyaxx </p><p> yyaxxyxP 0011 2equation with lineon the lies ,</p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y T lies on PT 1010 2 yyaxx </p><p>2 2 2Show that has equation 2QT xx a y y T lies on QT 2020 2 yyaxx </p><p> yyaxxyxP 0011 2equation with lineon the lies ,</p><p> yyaxxyxQ 0022 2equation with lineon thelies ,</p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y T lies on PT 1010 2 yyaxx </p><p>2 2 2Show that has equation 2QT xx a y y T lies on QT 2020 2 yyaxx </p><p> yyaxxyxP 0011 2equation with lineon the lies ,</p><p> yyaxxyxQ 0022 2equation with lineon thelies ,Hence the chord of contact is yyaxx 00 2</p></li><li><p>(2) Cartesian approach</p><p>1 1 1Show that has equation 2PT xx a y y T lies on PT 1010 2 yyaxx </p><p>2 2 2Show that has equation 2QT xx a y y T lies on QT 2020 2 yyaxx </p><p> yyaxxyxP 0011 2equation with lineon the lies ,</p><p> yyaxxyxQ 0022 2equation with lineon thelies ,Hence the chord of contact is yyaxx 00 2</p><p>Exercise 9H; 1c, 2d, 3, 6, 8, 10, 14</p><p>Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28</p></li></ul>