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in Mathematics by (53.3k points)

The locus of the midpoints of chords of the parabola y2 = 16x which passes through the vertex is a parabola whose length of latus rectum is

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Best answer

Let M(x1, y1) be the midpoint of a chord of y2 = 16x. Hence, the equation of the chord is

yy1 - 8(x +  x1) = y12  - 16x1 

This chord passes through the vertex (0, 0). This implies

- 8x1 = y12  - 16x1 

= y12  - 8x1 

Therefore, the locus of M(x1, y1) is the parabola y2 = 8x. Hence, the length of latus rectum is 8.

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