The equation of a tangent to the parabola $y^{2} = 9 x$ from the point $(4, 10)$ is

x - 4 y + 36 = 0

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81 x - 8 y - 162 = 0

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9 x - 4 y + 4 = 0

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x - 4 y - 36 = 0

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Solution

The correct options are
A $x - 4 y + 36 = 0$
D $9 x - 4 y + 4 = 0$
Equation of tangent is $y = m x + \frac{a}{m}$
Here $a = 9 / 4$
Hence the equation is $y = m x + \frac{9}{4 m}$
Now the line passes through $(4, 10)$
$10 = 4 m + \frac{9}{4 m}$
$16 m^{2} - 40 m + 9 = 0$
$m = \frac{1}{4}, \frac{9}{4}$
Option A and C

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