a point move in such away that its its distance from the x−axis is alwa yas(1/5) its distance from origin. find the equetion of its path.


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Question Number 43190 by MASANJA J last updated on 08/Sep/18

$a p o i n t m o v e i n s u c h a w a y t h a t i t s$ $i t s d i s t a n c e f r o m t h e x - a x i s i s a l w a$ $y a s \frac{1}{5} i t s d i s t a n c e f r o m o r i g i n .$ $f i n d t h e e q u e t i o n o f i t s p a t h .$
Commented by MrW3 last updated on 08/Sep/18

$\sin θ = \frac{1}{5}$ $\Rightarrow \tan θ = \frac{1}{\sqrt{24}} = k$ $e q n . :$ $y = \pm k x$ $w i t h k = \frac{1}{\sqrt{24}}$
	Answered by tanmay.chaudhury50@gmail.com last updated on 08/Sep/18

	$l e t t h e p o i n t b e (α, β)$ $\frac{1}{5} \sqrt{α^{2} + β^{2}} = β$ $α^{2} + β^{2} = 25 β^{2}$ $s o t h e l o c u s i s$ $\propto^{2} - 24 β^{2} = 0$ $x^{2} - 24 y^{2} = 0$
	Commented by tanmay.chaudhury50@gmail.com last updated on 08/Sep/18

	$y e s . . .$
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