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If the 4 points of intersection of lines $2 x − y + 1 = 0, x − 2 y + 3 = 0$ with the coordinate axes are concyclic then centre of circle passing through these points is

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7 / 4, 5 / 4

7 / 4, − 5 / 4

− 7 / 4, 5 / 4

− 74, − 54

answer is C.

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Detailed Solution

Equation of the circle is $(2 x - y + 1) (x - 2 y + 3) - 5 x y = 0 \Rightarrow 2 x^{2} + 2 y^{2} + 7 x - 5 y + 3 = 0 \Rightarrow x^{2} + y^{2} + \frac{7}{2} x - \frac{5}{2} y + \frac{3}{2} = 0 c e n t r e = (\frac{- 7}{4}, \frac{5}{4})$

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