Analysis and Approaches for IBDP Maths Ebook 2 | Page 147

Thus, the slope of normal
� �1�
1
�� 1
The equation of normal:
� � � �
y� � �1
x�
2 �
2 �
� �
� �
y� � �x�
2 2
�
x� y� 2 � 0
2
x� y� 2�
� 0
AG
A1
A1
[7]
11
Exercise 45
1. Show that the point (1,1) on the curve
2
y ln x x y
� � has a tangent with equation y� x.
[7]
2. Find the equation of normal on the curve
� 1 �
�1, �
� 2 � . [8]
5 � �5
2y arctan x � x � at the point
4 4
3. Find the equations of tangent on the curve
3
� .
8
x
�4y
� 100 where the slope of tangent is
2 2
[8]
4. Find the equations of normal on the curve
2 2
9x
y 106
� � where the slope of normal is
5
27 . [8]
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