Find the condition on ‘a’ & ‘b’ so that the two tangents drawn to the parabola y^2 = 4ax from a point are normals to the parabola x^2 = 4by.

Question

Find the condition on &lsquo;a&rsquo; & &lsquo;b&rsquo; so that the two tangents drawn to the parabola y^2 = 4ax from a point are normals to the parabola x^2 = 4by.

Himanshu Sharma · Answer

first find the slope of tangent to y^2=4ax

diff it to find he slope

2ydy=4adx

dy/dx=2a/y (ii)

similarly find slope of tangent to x^2=4by

2xdx=4bdy

dy/dx=x/2b

slope of normal=-1/slope of tangent

hence slope of normal=-2b/x -(i)

but (i)and (ii) are same

hence -2b/x=2a/y

by+ax=0

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Find the condition on ‘a’ & ‘b’ so that the two tangents drawn to the parabola y^2 = 4ax from a point are normals to the parabola x^2 = 4by.

Find the condition on ‘a’ & ‘b’ so that the two tangents drawn to the parabola y^2 = 4ax from a point are normals to the parabola x^2 = 4by.

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