Question

Angle between the tangents at $(0,0)$ to the curves $y^2=2015x$ and $x^2=2014$ y is __________.

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

Answer 1

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

Now compare given parabola $y^2=2015x$ with standard parabola $y^2=4ax$
$\therefore 4a=2015$
$\therefore a=\frac{2015}{4}>0$
$\therefore y^2=2015x$ is the parabola with X-axis as principles axis.
Hence symmetric about X-axis
$\therefore$ Tangent will be Y-axis $\left(1\right)$
Similarly $x^2=2014y$ is parabola as principle axis Y-acis
$\therefore$ X-axis will be its tangent
From the figure it is clear that angle between tangents at point $(0,0)$ is $\frac{\pi }{2}$.