The chords of contact of the pair of tangents drawn from points on the line 2x + y = 4 to the circle x2 + y2 = 1 passes through a fixed point M (a, b). Then find the value of \left(\right. \frac{1}{a} \textrm{ }\textrm{ } + \textrm{ }\textrm{ } \frac{1}{b} \left.\right).

Engineering

Mathematics

A Circle

Question

The chords of contact of the pair of tangents drawn from points on the line 2x + y = 4 to the circle x² + y² = 1 passes through a fixed point M (a, b). Then find the value of $(\frac{1}{a} + \frac{1}{b})$ .

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Clearly, equation of chord of contact is
(4y – 1) + t (x – 2y) = 0, t $\in$ R
⇒ L₁ + t L₂ = 0, t $\in$ R
$∴$ M (a, b) = $(\frac{1}{2}, \frac{1}{4})$
Hence, $(\frac{1}{a} + \frac{1}{b})$ = 2 + 4 = 6.

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