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Question Number 119875 by help last updated on 27/Oct/20

Commented by help last updated on 27/Oct/20

$t h x . . . s a m e a n s w e r . n o c o r r e c t o p t i o n s$
	Answered by TANMAY PANACEA last updated on 27/Oct/20

	$3 y + 2 x - 24 = 0$ $d j =∣ \frac{3 \times 3 + 2 \times 1 - 24}{\sqrt{3^{2} + 2^{2}}} ∣=∣ \frac{- 13}{\sqrt{13}} ∣= \sqrt{13} s o r r y i m a d e m i s t a k e$
	Answered by Dwaipayan Shikari last updated on 27/Oct/20

	$y = - \frac{2}{3} x + 8$ $3 y + 2 x - 24 = 0$ $P \equiv (1, 3)$ $D i s t a n c e = \frac{∣ 3.3 + 2.1 - 24 ∣}{\sqrt{3^{2} + 2^{2}}} = \frac{13}{\sqrt{13}} = \sqrt{13}$
	Answered by mr W last updated on 27/Oct/20

	$D = d^{2} = {(x - 1)}^{2} + {(y - 3)}^{2} = {(x - 1)}^{2} + {(- \frac{2}{3} x + 8 - 3)}^{2}$ $\frac{d D}{d x} = 2 (x - 1) + 2 (- \frac{2}{3} x + 5) (- \frac{2}{3}) = 0$ $9 x - 9 + 4 x - 30 = 0$ $\Rightarrow x = 3$ $d_{m i n} = \sqrt{{(3 - 1)}^{2} + {(- \frac{2}{3} \times 3 + 5)}^{2}} = \sqrt{13}$
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