Question

The equation of a tangent to the parabola, $x^2=8y$, which makes an angle $\theta$ with the positive direction of x-axis, is:

• A. $x=ycot\theta +2tan\theta$
• B. $x=ycot\theta -2tan\theta$
• C. $x=xtan\theta -2cot\theta$
• D. $x=xtan\theta +2cot\theta$

Answer 1

The correct option is A $x=ycot\theta +2tan\theta$

$x^2=y$

$\Rightarrow \frac{dy}{dx}=\frac{x}{4}=tan\theta$

$\therefore x_1=4tan\theta$

$y_1=2ta{n}^2\theta$

Equation of tangent:-

$y-2ta{n}^2\theta =tan\theta (x-4tan\theta )$

$\Rightarrow x=ycot\theta +2tan\theta$