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The point of intersection of the tangent to the parabola $y^{2} = 4 x$ at the points where the circle ${(x - 3)}^{2} + y^{2} = 9$ meets the parabola, other than the origen, is

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$(- 1, - 1)$

$(- 1, 0)$

$(- 2, 0)$

$(0, 1)$

answer is D.

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Detailed Solution

${(x - 3)}^{2} + 4 x = 9$

$\Rightarrow x^{2} - 2 x = 0 \Rightarrow x = 2, x = 0$

$∴ y = \pm 2 \sqrt{2}$

$∴$ equation of tangent of $(2, \pm 2 \sqrt{2})$

$y (2 \sqrt{2}) = 2 (x + 2) & y - 2 \sqrt{2} = 2 (x + 2)$

$∴ x = - 2, y = 0$

. $∴ (- 2, 0)$

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