Question

The length of the line segments joining focus to the point of intersection of angular bisector of co-ordinate axes (in the first quadrant) and the parabola $y^2=lx$ is

• A. $\frac{l}{4}$
• B. $2l$
• C. $\frac{5l}{4}$
• D. $l\sqrt{2}$

Answer 1

Answer: (A), (C)

The correct options are
A $\frac{l}{4}$
C $\frac{5l}{4}$

Equation of angular bisector of co-ordinate axes is $y=x$
It cuts the parabola $y^2=lx$ at $A(l,l)$ and $B(0,0)$
Here, the focus of the parabola is $S(\frac{l}{4},0)$
$\therefore$ Required length of line segments are $SA$ and $SB$ i.e. $\frac{5l}{4}$ and $\frac{l}{4}$