KCET · Maths · Parabola
The sum of the reciprocals of focal distances of a focal chord \(P Q\) of \(y^{2}=4 a x\) is
- A \(\frac{1}{a}\)
- B \(a\)
- C \(2 a\)
- D \(\frac{1}{2 a}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{a}\)
Step-by-step Solution
Detailed explanation
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
\[
=\frac{1}{2 a}+\frac{1}{2 a}=\frac{2}{2 a}=\frac{1}{a}
\]
Total length of focal chord \(=4 a\)
and half length of focal chord \(=2 a\)
Now, sum of the reciprocals of focal distances
\[
=\frac{1}{2 a}+\frac{1}{2 a}=\frac{2}{2 a}=\frac{1}{a}
\]
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