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Q.

The distance of the point $(2, 3)$ from the line $4 x - 3 y + 26 = 0$ is same as its distance from the line $3 x - 4 y + p = 0$ . The value of $p$ can be

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a

5

b

25

c

31

d

$- 31$

answer is C.

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Detailed Solution

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We have
$\begin{array}{l} |\frac{4 \times 2 - 3 \times 3 + 26}{\sqrt{4^{2} + 3^{2}}}| = |\frac{3 \times 2 - 4 \times 3 + p}{\sqrt{4^{2} + 3^{2}}}| \\ \Rightarrow \pm 25 = 6 - 12 + p \\ \Rightarrow p = \pm 25 + 6 \end{array}$
$\Rightarrow p = 31$ or $- 19 .$

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