Q.12.The angle between the tangents to the curves y=2x2 and x=2y2 at (1,1) is
A. tan^{-1}\left ( \frac{15}{8} \right )
B. tan^{-1}\left ( \frac{7}{8} \right )
C. tan^{-1}\left ( \frac{3}{4} \right )
D. tan^{-1}\left ( \frac{1}{4} \right )
Answer :- A. tan^{-1}\left ( \frac{15}{8} \right )
Explanation :-
y=2x2
Slope of the tangent to this curve is
\frac{dy}{dx}=m_{1}=4xat (1,1), m1=4
x=2y2
Slope of the tangent to this curve is \frac{dy}{dx}=m_{2}=\frac{1}{4y}
at (1,1), m2= \frac{1}{4}
Let \theta be the angle between two tangents
tan\; \theta =\left | \frac{m_{1}-m_{2}}{1+m_{1}m_{2}}\right | tan\; \theta =\left | \frac{4-\frac{1}{4}}{1+4\times \frac{1}{4}}\right |=\frac{15}{8} \theta =tan^{-1}\left ( \frac{15}{8} \right )