Find locus of a point P which moves such that its distance from the line y=(√3)x−7 is same as its distance from (2(√3),−1) ?


Question and Answers Forum

All Questions Topic List
Coordinate Geometry Questions
Previous in All Question Next in All Question
Previous in Coordinate Geometry Next in Coordinate Geometry
Question Number 47438 by rahul 19 last updated on 10/Nov/18

$F i n d l o c u s o f a p o i n t P w h i c h m o v e s$ $s u c h t h a t i t s d i s t a n c e f r o m t h e l i n e$ $y = \sqrt{3} x - 7 i s s a m e a s i t s d i s t a n c e f r o m$ $(2 \sqrt{3}, - 1) ?$
	Answered by ajfour last updated on 10/Nov/18

	$\frac{{(y - x \sqrt{3} + 7)}^{2}}{4} = {(x - 2 \sqrt{3})}^{2} + {(y + 1)}^{2}$ $y^{2} + 3 x^{2} + 49 - 2 \sqrt{3} x y - 14 \sqrt{3} x$ $+ 14 y = 4 x^{2} + 4 y^{2} - 16 \sqrt{3} x + 8 y + 52$ $\Rightarrow x^{2} + 3 y^{2} + 2 \sqrt{3} x y - 2 \sqrt{3} x - 6 y + 3 = 0$ $\Rightarrow {(x + \sqrt{3} y)}^{2} - 2 \sqrt{3} (x + \sqrt{3} y) + 3 = 0$ $\Rightarrow {(x + \sqrt{3} y - \sqrt{3})}^{2} = 0$ $\Rightarrow \sqrt{3} y = \sqrt{3} - x .$
	Commented by rahul 19 last updated on 10/Nov/18
	thanks sir��
	Answered by rahul 19 last updated on 10/Nov/18

	$s i n c e t h e p o i n t s a t i s i f e s t h e l i n e .$ $l o c u s i s s t . l i n e p e r p e n d i c u l a r t o g i v e n$ $l i n e p a s s i n g t h r o u g h g i v e n p o i n t .$ $\Rightarrow l o c u s = (y + 1) = - \frac{1}{\sqrt{3}} (x - 2 \sqrt{3}) .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum