25[(x−2)^2 +(y−3)^2 ]=(3x−4y+7)^2 is the equation of parabola.Find length of latus rectum


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Question Number 31846 by momo last updated on 15/Mar/18

$25 [{(x - 2)}^{2} + {(y - 3)}^{2}] = {(3 x - 4 y + 7)}^{2}$ $i s t h e e q u a t i o n o f p a r a b o l a . F i n d$ $l e n g t h o f l a t u s r e c t u m$
Commented by momo last updated on 16/Mar/18

$h o w$
Commented by momo last updated on 16/Mar/18

$e x p l a i n w i t h {s o l}^{n}$
	Answered by Tinkutara last updated on 16/Mar/18

	${(x - 2)}^{2} + {(y - 3)}^{2} = {(\frac{3 x - 4 y + 7}{5})}^{2}$ $\sqrt{{(x - 2)}^{2} + {(y - 3)}^{2}} =∣ \frac{3 x - 4 y + 7}{5} ∣$ $F o c u s = (2, 3)$ $D i r e c t r i x i s 3 x - 4 y + 7 = 0$ $D i s t a n c e o f f o c u s f r o m d i r e c t r i x = 2 a$ $2 a =∣ \frac{6 - 12 + 7}{5} ∣= \frac{1}{5}$ $4 a = \frac{2}{5}$
	Commented by momo last updated on 16/Mar/18

	$t h a n k s s i r$
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