The parabolas y2=4ax and x2=4by intersect orthogonally at point P(x1,y1) where x1,y1 is not equal to 0 then find the relation between a and b.(A)b=a2(B)b=a3(C)b3=a2(D)None of these

Dear Jayati

y²=4ax

x²=4by

solve the curve for point of intersection

 x1 =4(ab²)^1/3

 y1 =4(ba²)^1/3

now slope of tangent at these points are

slope on curve y²=4ax , m1 =2a/y1

slope on curve x²=4by , m2 =x1/2b

m1 * m2 =-1

 ax1/by1 =-1

 a4(ab²)^1/3/b4(ba²)^1/3=-1

  a² +b² =0

which is not possible

so option d is correct

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