If (a, b) is the midpoint of a chord passing | vedclass

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(D) Let the vertex of the parabola $y^2 = 4x$ be $O(0, 0)$.Let the other end of the chord passing through the vertex be $P(h, k)$.Since $P(h, k)$ lies

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$2a = b^2$

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(D) Let the vertex of the parabola $y^2 = 4x$ be $O(0, 0)$.Let the other end of the chord passing through the vertex be $P(h, k)$.Since $P(h, k)$ lies on the parabola,we have $k^2 = 4h$.The midpoint $(a, b)$ of the chord $OP$ is given by $a = \frac{0+h}{2} = \frac{h}{2}$ and $b = \frac{0+k}{2} = \frac{k}{2}$.This implies $h = 2a$ and $k = 2b$.Substituting these into the parabola equation $k^2 = 4h$,we get $(2b)^2 = 4(2a)$.$4b^2 = 8a$,which simplifies to $b^2 = 2a$ or $2a = b^2$.

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

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