The equation of line passing through $(3, 4)$ and parallel to $5 x + 9 y + 12 = 0$ is

5 x - 9 y + 51 = 0

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5 x - 9 y - 51 = 0

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5 x + 9 y + 51 = 0

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5 x + 9 y - 51 = 0

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Solution

The correct option is D $5 x + 9 y - 51 = 0$
Given line $5 x + 9 y + 12 = 0$
Line parallel to this
$5 x + 9 y + λ = 0$
It passes through $(3, 4)$ , we get
$15 + 36 + λ = 0 \Rightarrow λ = - 51$
Therefore the required equation of line is
$5 x + 9 y - 51 = 0$

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