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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

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

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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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Badiuddin

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