Find the locus of the middle point of focal chord of parabola whose eq. is Y^2=4aX(standard eq.)

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Please find below the solution to the asked query:

We have y2=4axWe know that ends of focal chord are at2,2at and at2,-2atLet h,k be the mid point of the chord.k=2at+-2at22k=2at-2at2k=2at-1tt-1t=ka ;ih=at2+at222h=at2+at22ha=t2+1t22ha=t-1t2+2   a2+b2-2ab=a-b22ha=ka2+22ha=k2a2+22ah=k2+2a2To get equation of locus, replacehx and ky2ax=y2+2a2y2=2ax-a

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