Write the equation of pair of tangents to the parabola $y^{2} = 4 x$ drawn from a point P(-1, 2)

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Solution

We know the equation of pair of tangents are given by $S S_{1} = T^{2}$
$∴ (y^{2} - 4 x) (4 + 4) = (2 y - 2 (x - 1))^{2}$
$\Rightarrow 8 y^{2} - 32 x = 4 y^{2} + 4 x^{2} + 4 - 8 x y + 8 y - 8 x$
$\Rightarrow y^{2} - x^{2} + 2 x y - 6 x - 2 y = 1$

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