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.

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

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