Find the condition that the straight line $a x + b y + c = 0$ touches the parabola $y^{2} = 4 k x$ .

k b^{2} = a c

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k c^{2} = a b

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k a^{2} = b c

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n o n e o f t h e s e

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Solution

The correct option is A $k b^{2} = a c$
Given line may be written as $y = - \frac{a}{b} x - \frac{c}{b}$
Using condition of tangency, $c = \frac{a}{m}$
$\Rightarrow - \frac{c}{b} = \frac{k}{- \frac{a}{b}}$
$\Rightarrow k b^{2} = a c$

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