Question

The equation of the directrix of the parabola with vertex at the origin and having the axis along $x$ − axis and a common tangent of slope $2$ with the circle $x^2+y^2=5$ is⁄are

• A. $x=10$
• B. $x=20$
• C. $x=-10$
• D. $x=-20$

Answer 1

Answer: (A), (C)

The correct options are
A $x=10$
C $x=-10$

The line $y=2x+c$ is a tangent to $x^2+y^2=5$.
If $c^2=25$, then $c=\pm 5$.
Let the equation of the parabola be $y^2=4ax$. Then $\frac{a}{2}=\pm 5$
or $a=\pm 10$
So, the equation of the parabola is $y^2=\pm 40x$.
Also, the equations of the directrices are $x=\pm 10$.