The midpoints of focal chords of y^2 = 16x is?  [Ans: y^2 = 8(x-4)]

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Please find below the solution to the asked query:

I assume you need locus of mid point of focal chord. We havey2=16xCompare with y2=4ax4a=16a=4Ends of focal chord are Aat2,2at and Bat2,-2atA4t2,8t and B4t2,-8tLet mid point of focal chord be h,k 2k=8t-8t2k=8t-1tk4=t-1t...i2h=4t2+4t2 2h=4t2+1t2h2=t2+1t2h2=t-1t2+2Use ih2=k42+2h2=k216+2h=k28+4k28=h-4k2=8h-4Hence locus isy2=8x-4

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