A tangent is drawn at any point P(t) on the parabola `y^(2)=8x` and on it is takes a point `Q(alpha,beta)` from which a pair of tangent QA and QB are drawn to the circle `x^(2)+y^(2)=8`. Using this information, answer the following questions : The point from which perpendicular tangents can be drawn both the given circle and the parabola is

Options

A. `(4,pmsqrt(3))`
B. `(-1,sqrt(2))`
C. `(-sqrt(2),-sqrt(2))`
D. `(-2,pm2sqrt(3))`

Answer

D

Explanation

(4)
the required point `(x_(1),y_(1))` will lie on the director circle of the given circle as well as on the directrix of parabola. Therefore,
`x_(1)^(2)+y_(1)^(2)=16andx_(1)+2=0`
`or4+y_(1)^(2)=16`
`ory=pm2sqrt(3)`
Therefore, the points are `(-2,pm2sqrt(3))`.