If $(a, b)$ is the midpoint of a chord passing through the vertex of the parabola $y^{2} = 4 x$ , then

a = 2 b

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2 a = b

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a^{2} = 2 b

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2 a = b^{2}

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Solution

The correct option is D $2 a = b^{2}$
Given equation of parabola is $y^{2} = 4 x$
Let $P (t^{2}, 2 t)$ be the other end-point of the chord of the parabola.
Then , $a = \frac{t^{2}}{2}$ and $b = \frac{2 t}{2}$
$\Rightarrow a = \frac{b^{2}}{2}$
or $b^{2} = 2 a$

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The correct option is D 2a=b2Given equation of parabola is y2=4xLet P(t2,2t) be the other end-point of the chord of the parabola.Then , a=t22 and b=2t2⇒a=b22or b2=2a

If $(a, b)$ is the midpoint of a chord passing through the vertex of the parabola $y^{2} = 4 x$ , then

The correct option is D $2 a = b^{2}$
Given equation of parabola is $y^{2} = 4 x$
Let $P (t^{2}, 2 t)$ be the other end-point of the chord of the parabola.
Then , $a = \frac{t^{2}}{2}$ and $b = \frac{2 t}{2}$
$\Rightarrow a = \frac{b^{2}}{2}$
or $b^{2} = 2 a$