Analysis and Approaches for IBDP Maths Ebook 2 | Page 144

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. A curve C is given by the implicit equation
2 2
5x 2xy 3y 16x
0
� � � � .
(a) Show that d y 5 x �y
�
�
8 .
dx x � 3y
Q and R are two different points on C such that the normals of C at Q and R has
gradient
1
� .
5
(b) Find the coordinates of Q and R .
(c)
Find the range of values of y if
� d y dy
dx
� � dx
.
2
( x
2
3 y) 2
8(3 2 x)
[4]
[6]
[6]
4. A curve C is given by the implicit equation
x xy 8 y
2
� � � .
(a) Show that d y 1 � y
�
dx 2y � x
. [4]
P and Q are two different points on C such that the normals of C at P and Q are
horizontal.
(b) Find the coordinates of P and Q .
(c) Show that
2
2
d y 1 d y ( x �2)( y �1)
� �
� 0
2 � � � � .
3
dx 1�
y �d x � (2 y �x)
[7]
[6]
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