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

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

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Jayati

y2=4ax

x2=4by

 

if these curve intersec orthogonally ,then tangent at heir point of intersection will also intersect orthogonall

 slope of tangent at y2=4ax  is  m1 = 2a/y1 

 sinece y1=0 so tangent is y axis

 

slope of tangent at x2=4by  is  m2 = x1/2b 

 sinece x1=0 so tangent is x axis

so these two tangent is perpendicular

 so these curve always intersect for all value of a,b

Please feel free to post as many doubts on our discussion forum as you can.
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Regards,
Askiitians Experts
Badiuddin

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