The equation of the directrix of the parabola with vertex at the origin and having the axis along the x-axis and a common tangent of slope 2 with the circle `x^2+y^2=5` is (are) `x=10` (b) `x=20` `x=-10` (d) `x=-20`

Options

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

Answer

A, C

Explanation

1,3 The line y=2x+c ix a tangent to `x^(2)+y^(2)=5`.
If `c^(2)=25`, then `c=pm5`.
Let the equation of the parabola be `y^(2)=4ax`. Then
`(a)/(2)=pm5`
`ora=pm10`
So, the equation of the parabola is `y^(2)=pm40x`.
Also, the equation of the directrices are `x=pm10`.