Question

Angle between the tangents at $(0,0)$ to the curves $y^2=32x$ and $x^2=108y$ is ______

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

Answer 1

Answer: (B)

$\frac{\pi }{2}$

Slope of a tangent is given by $\frac{dy}{dx}$

For $y^2=32x$

$2y\frac{dy}{dx}=32$

slope$=m_1=\frac{16}{y}=\infty$ at $(0,0)$

Hence, tangent will be along $Y-axis$.

For $x^2=108y$

$2x=108\frac{dy}{dx}$

slope$=m_2=\frac{x}{54}=0$ at $(0,0)$

Hence, tangent will be along $X-axis$.

And, thus angle between the tangents is $\frac{\pi }{2}$ as Y and X-axis are perpendicular to each other.