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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.
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 by+ax=0
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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