Q92 / 180 · KCET 2011 · Mathematics
The sum of the reciprocals of focal distances of a focal chord $P Q$ of $y^{2}=4 a x$ is
- Correct answerA$\frac{1}{a}$
- B$a$
- C$2 a$
- D$\frac{1}{2 a}$
Solution
Equation of parabola $y^{2}=4 a x$
Total length of focal chord $=4 a$
and half length of focal chord $=2 a$
Now, sum of the reciprocals of focal distances
$$
=\frac{1}{2 a}+\frac{1}{2 a}=\frac{2}{2 a}=\frac{1}{a}
$$
Hence, the correct answer is option: 'A'.