Find the equation of the chord of contact of tangents to the parabola
$y^{2} = 4 x$ from the point $P (3, 4)$ .

$x - 2 y - 6 = 0$

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$x + 2 y + 6 = 0$

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$x + y + 3 = 0$

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$x - 2 y - 3 = 0$

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Solution

The correct option is D
$x - 2 y - 3 = 0$

Equation to the chord of contact of tangents drawn from the point $P (x_{1}, y_{1})$ is T = 0

$y y_{1} - 2 a (x + x_{1}) = 0$

Here,

$x_{1} = 3 y_{1} = 4$

$y (4) - 2 (x + 3) = 0$

$4 y - 2 x + 6 = 0$

$2 x - 4 y - 6 = 0$ or $x - 2 y - 3 = 0$

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