The equation of tangent drawn from the point $A (2 a, 3 a)$ to the parabola $y^{2} = 4 a x$ is?

x - y + a = 0

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x - 2 y + 4 a = 0

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x - 3 y + 9 a = 0

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x - 4 y + 16 a = 0

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Solution

The correct option is B $x - 2 y + 4 a = 0$
Equation of parabola $= y^{2} = 4 a x$

$point = (2 a, 3 a)$

Equation of tangent at parabola $y^{2} = 4 a x$ having slope $m$ ;

$y = m x + \frac{a}{m}$

Put the known values

$3 a = 2 a m + \frac{a}{m}$
$3 a m = 2 a m^{2} + a$
$2 a m^{2} - 3 a m + a = 0$
$m = 1, 1 / 2$

So, the possible equation for tangent are,

$y = x + a; y = \frac{x}{2} + 2 a$

$2 y = x + 4 a$
$x - 2 y + 4 a = 0$

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