The length of the latus rectum of the parabola $x = a y^{2} + b y + c$ is

\frac{a}{4}

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\frac{a}{3}

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\frac{1}{a}

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\frac{1}{4 a}

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Solution

The correct option is C $\frac{1}{a}$
Given,

$x = a y^{2} + b y + c$

$a y^{2} + b y = x - c$

$a {(y + \frac{b}{a})}^{2} = x + \frac{a b^{2}}{4} - c$

${(y + \frac{b}{a})}^{2} = \frac{1}{a} (x + \frac{a b^{2}}{4} - c)$

Length of latus rectum $= \frac{1}{a}$

Suggest Corrections

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