Tangents And Normals

Given,

On differentiating both sides w.r.t. , we get

and

Slope of tangent will be
Since, the tangent is parallel to line .




When , then
When , then
Now, equation of tangents at point is



...(i)
and equation of tangents at point is




...(ii)
Hence, Eqs. (i) and (ii) are required equations of the tangents.

Given,


Slope of tangent to the curve (i)

Slope of tangent at point is

Given, tangent of curve (i) is parallel to line (ii).
Slope of line (ii) is 4 .
From E (iii), we get


lie on curve (i).


Points are and