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Point Form of Tangent: Ellipse

The line x+y+...

Question

The line x+y+2 = 0 is a tangent to a parabola $y^{2} = 4 a x$ at point A, it intersects the directrix at B and tangent at vertex at C, then (AC $\times$ BC) =

A

8

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B

4

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C

12

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D

16

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Solution

The correct option is A
8

$a m^{2} = l n \Rightarrow a {(1)}^{2} = 1 \times 2 \Rightarrow a = 2$

A = (2, -4), B = (-2, 0), C = (0, -2) $\Rightarrow$ AC . BC = 8

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