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Find the locus of midpoint of variable chord of parabola y2 = 4ax such that tangents make an angle Φ between them.
Dear Priyansh
let the mid point is (h,k)
and let the point where tangent touch the parabola is (at12,2at1) and (at22,2at2)
so 2h = a(t12 + t22) and 2k = 2a(t1+t2) ...................1
from equation 1 find the value of t1t2 = (k2 -2ha)/2a2
and |t1-t2| = 1/a {k2 - 4ha}1/2
so given tanΦ = |m1-m2|/(1+m1m2)
where m1 = 1/t1
m2 =1/t2
so put these value
tanΦ =2a{k2 -4ha}1/2 / {k2 -2ha}
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