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Question

Mathematics Question on Conic sections

The sum of the reciprocals of focal distances of a focal chord PQPQ of y2=4axy^2 = 4ax is

A

1a\frac {1}{a}

B

aa

C

2a2a

D

12a\frac {1}{2a}

Answer

1a\frac {1}{a}

Explanation

Solution

Equation of parabola y2=4axy^{2}=4 ax Total length of focal chord =4a=4 a and half length of focal chord =2a=2 a Now, sum of the reciprocals of focal distances =12a+12a=22a=1a=\frac{1}{2 a}+\frac{1}{2 a}=\frac{2}{2 a}=\frac{1}{a}