Find the locus of the midpoints of the chords | vedclass

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(A) The equation of the chord of a parabola $S = 0$ with midpoint $(h, k)$ is given by $T = S_1$.For the parabola $x^2 + 4y = 0$,the equation of the c

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$x^2 + 2y + 2 = 0$

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(A) The equation of the chord of a parabola $S = 0$ with midpoint $(h, k)$ is given by $T = S_1$.For the parabola $x^2 + 4y = 0$,the equation of the chord with midpoint $(h, k)$ is $xh + 2(y + k) = h^2 + 4k$.Since the chord passes through the focus $(0, -1)$,we substitute these coordinates into the equation:$x(0) + 2(-1 + k) = h^2 + 4k$$-2 + 2k = h^2 + 4k$$h^2 + 2k + 2 = 0$.Replacing $(h, k)$ with $(x, y)$,the locus is $x^2 + 2y + 2 = 0$.

Find the locus of the midpoints of the chords of the parabola $x^2 + 4y = 0$ which pass through its focus.

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