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The mid-point of A variable chord AB of the parabola y 2 =4ax lies on the line y=ka, where k is A constant, then find the equation of the locus of the points of intersection of tangents at A and B.
Let A is (at1square ,2at1) and B is (at2square ,2at2) .Ordinate of midpoint of these points will satisfy y=Ka .so we get t1+t2=K. Let point of locus is (alpha,beta). Now we know in parabola point of intersection of tangents can be written as (at1t2, at1+at2). So beta=at1+at2 .put value of t1+t2=k.so we get beta=Ka .now replace beta with y .so required locus is y=Ka.
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