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Equation of t...

Question

Equation of the circle on the line joining the points $(1, - 3)$ and $(2, 5)$ as diameter is

A

x^{2} + y^{2} - 3 x - 2 y - 13 = 0

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B

x^{2} + y^{2} + 3 x + 2 y - 15 = 0

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C

x^{2} + y^{2} - 3 x + 2 y - 13 = 0

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D

x^{2} + y^{2} + 3 x - 2 y - 13 = 0

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Solution

The correct option is A $x^{2} + y^{2} - 3 x - 2 y - 13 = 0$
Given,

$(1, - 3), (2, 5)$ as diameter,

we have, the formula,

$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$

$(x - 1) (x - 2) + (y + 3) (y - 5) = 0$

$x^{2} - 3 x + 2 + y^{2} - 2 y - 15 = 0$

$x^{2} + y^{2} - 3 x - 2 y - 13 = 0$

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