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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 x2+y2=5 is⁄are

A
x=10
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B
x=20
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C
x=10
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D
x=20
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Solution

The correct option is C x=10
The line y=2x+c is a tangent to x2+y2=5.
If c2=25, then c=±5.
Let the equation of the parabola be y2=4ax. Then a2=±5
or a=±10
So, the equation of the parabola is y2=±40x.
Also, the equations of the directrices are x=±10.

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