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
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`
A. x=10
B. x=20
C. x=-10
D. x=-20
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Correct Answer - A::C
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`.
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