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Problem 13

A and \(B\) are two points whose co-ordinates are \(\left(a t^{2}, 2 a t\right)\) and \(\left(\frac{a}{t^{2}},-\frac{2 a}{t}\right)\) and \(S\) is the point $(a, 0)\(. Prove that \)\frac{1}{S A}+\frac{1}{S B}=\frac{1}{a}$.

Expert verified

The value of \(\frac{1}{SA} + \frac{1}{SB}\) is indeed equal to \(\frac{1}{a}\), thus proving the given statement.

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