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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.

Priyansh Goel , 14 Years ago
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Badiuddin askIITians.ismu Expert

Last Activity: 14 Years ago

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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