Question

Consider the curve $x=1-3t^2,y=t-3t^3$, Let P(-2, 2) be a point on the curve. Let the tangent at P
cuts the curve again at Q. Then answer the following
The angle between the tangents at P and Q will be

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{6}$

Answer 1

The correct option is A $\frac{\pi }{2}$

Slope of tangent at $P_1{m}_1=\frac{-4}{3}$
Slope of tangent at Q, $m_2=\frac{3}{4}$
$m_1{m}_2=-1\Rightarrow$ angle is $\frac{\pi }{2}$