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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h = a t 2 + a 2 , k = 2 a t + 0 2 ⇒ t 2 = 2 h - a a and t = k a ⇒ k 2 a 2 = 2 h - a a ⇒ Locus of h , k is y 2 = a 2 x - a ⇒ y 2 = 2 a x - a 2 Its directrix is x - a 2 = - a 2 ⇒ x = 0

Mathematics - Parabola Question with Solution | TestHub

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