Parabola

Given equation of parabola is

On differentiating both sides, we get


Slope of tangent at point
and slope of normal at point
Since, normal makes equal angle with both and -axes, then



Now, when , then
when , then
So, the required point is

Given equation of parabola is

By putting in E (i), we get
and
Points on the parabola are and
Equation of the chord of given parabola by joining the points and will be



Now, equation of tangent parallel to chord will be

In given options, only option (b) satisfies the condition for E (iii)
i.e.