Director Circ...

Director Circle

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AB is a chord of the parabola $y^{2} = 4 a x$ with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-

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Q. If

S : x^{2} + y^{2} = 9

be a circle.

P A

and

P B

are pair of tangents on

S

where

P

is any point on the director circle of

S

, then the radius of the smallest circle which touches

S

externally and also the two tangents

P A

and

P B

α + β \sqrt{2}

. Then the value of

α + β

is:

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The chord AB of the parabola $y^{2} = 4 a x$ cuts the axis of the parabola at C. If $A = (a t_{1}^{2}, 2 a t_{1}), B = (a t_{2}^{2}, 2 a t_{2})$ and AC : AB = 1:3 then

$t_{2} = 2 t_{1}$
$t_{2} + 2 t_{1} = 0$
$t_{1} + 2 t_{2} = 0$
None of these

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