It would be very kind if you give me the solutions of the following questions=Q1.a,b,c are positive numbers in GPand the equation (a+di)x2 +2(b+ei)x +(c+if) =0 have only one real root then a/c , b/e , c/f are in HP/GP/AP? (i=iorta)Q2.Length of shortest normal chord of y2 =4x is ?Q3.Let P be a point on the ellipse (x-2y+3)2/125 + (2x+y-1)2 /45 =1 and A and B are the foci of the ellipse. Find the maximum area of triangle ABP.

Dear Aman,

TAKE GENERAL POINT (at²,2at)

find dydx at this point
then slope of normal =- dxdy

then find  equation of normal----
suppose it again intersect at 
(at²₁,2at₁)

find the condition between t and  t₁

find length of chord =L

then find dL/dt

Best Of luck

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