Question

Let F be the focus of the parabola y2 = 4ax and M be the foot of perpendicular from point P(at2, 2at) on the tangent at the vertex. If N is a point on the tangent at P then $\frac{MN}{FN}$ equals-

• A. $\frac{t^{2}}{t^{2} + 1}$
• B. $\frac{t^{2} + 1}{t^{2}}$
• C. 1
• D. None of these

Answer 1

Answer: (A)

$\frac{t^{2}}{t^{2} + 1}$

Answer 2

The tangent at any point P on the parabola bisects the angle between the focal chord through P and the line parallel to the axis.

\ $\frac{MN}{FN}$ = $\frac{at^{2}}{at^{2} + a} = \frac{t^{2}}{t^{2} + 1}$ .