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If the four p...

Question

If the four points of intersection of the lines $(2 x - y + 1) (x - 2 y + 3) = 0$ with the axes lies on a circle, then find its centre.

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Solution

Apply the condition that $S - λ x y = 0$ represents a circle where $x y = 0$ represents the equation of axes. $∴ λ = - 5$ .
$2 x^{2} + 2 y^{2} + 7 x - 5 y + 3 = 0$ , centre $(- 7 / 4, 5 / 4)$ .

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