The equation of diameter of a circle $x^{2} + y^{2} + 2 x - 4 y = 4$ , that is parallel to 3x+5y=4 is

3x+5y=7

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3x-5y=7

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3x+5y=-7

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3x-5y=-7

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Solution

The correct option is A 3x+5y=7
$x^{2} + y^{2} + 2 x - 4 y - 4 = 0$
$c e n t e r \equiv (- 1, 2)$
$∴$ diameter has to parallel to $3 x + 5 y = 4$
let equation be $3 x + 5 y = λ$
passes through $(- 1, 2)$
$∴ 3 \times (- 1) + 5 \times 2 = λ$
$\Rightarrow λ = - 3 + 10 = 7$
$∴ e q u a t i o n \Rightarrow 3 x + 5 y = 7$

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