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

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Solution

The correct option is A 8
$a m^{2} = l n \Rightarrow a (1)^{2} = (1) (2) \Rightarrow a = 2$
$∴ A = (2, - 4), B = (- 2, 0), C = (0, - 2) \Rightarrow A C . B C = 8$

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