The locus of the mid-point of the line segment joining the focus of the parabola y 2 = 4 a x to a moving point of the parabola, is another parabola whose directrix is:

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Aicharya · Accepted Answer

h = a t 2 + a 2 , &#160; k = 2 a t + 0 2 &#8658; &#160;&#160; t 2 = 2 &#160; h - a a and t = k a &#8658; &#160;&#160; k 2 a 2 = 2 &#160; h - a a &#8658; Locus of h , &#160; k is y 2 = a 2 x - a &#8658; &#160;&#160; y 2 = 2 a x - a 2 Its directrix is x - a 2 = - a 2 &#8658; x = 0

The locus of the mid-point of the line segment joining the focus of the parabola y 2 = 4 a x to a moving…

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