Analysis and Approaches for IBDP Maths Ebook 2 | Page 143

Exercise 44
1. A curve C is given by the implicit equation
x
e y
x � .
2
�12
� y , 6
(a) Show that d x
y e y
�� .
x
dx e � 2y
(b) The straight line L :3x � 7y
� 21 � 0 intersects C at P .
[4]
(i) Find the coordinates of P .
(c)
(ii) Hence, find the gradient of the tangent at P .
[6]
Q is a point on C where C intersects with the negative y -axis. Find the gradient
of the normal at Q .
[4]
2. A curve C is given by the implicit equation
2 2
2x axy y 56
� � � , a� .
(a) Show that d y 4 x � ay
�� .
dx ax � 2y
(b) The straight line L : x � y � 4 � 0 is the normal of C at P(2, � 6) .
(i) Write down the gradient of the normal at P .
[4]
10
(ii) Hence, find the value of a .
Q and R are two different points on C such that the tangents of C at Q and R are
horizontal.
(c) Show that the coordinates of Q and R are (2, 8) and ( �2, � 8) .
[5]
[5]
www.seprodstore.com
133