If sum of distances of a pointegral from the origin and line... | MATH - TRANSFORMATION OF AXES AND LOCUS | SolveeIt

If sum of distances of a point from the origin and lines $x = 2$ is 4, then its locus is.

$x^{2} - 12y = 36$

$y^{2} + 12x = 36$

$y^{2} - 12x = 36$

$x^{2} + 12y = 36$

Answer

$y^{2} + 12x = 36$

Explanation

Let point be $P ( x , y )$ . So, distance from the origin $O P = \sqrt { x ^ { 2 } + y ^ { 2 } }$ and distance from the line $= ( x - 2 )$

$\therefore \sqrt { x ^ { 2 } + y ^ { 2 } } + ( x - 2 ) = 4 \Rightarrow \sqrt { x ^ { 2 } + y ^ { 2 } } = ( - x + 6 )$

$\Rightarrow x ^ { 2 } + y ^ { 2 } = x ^ { 2 } + 36 - 12 x \Rightarrow y ^ { 2 } + 12 x = 36$ .

Question: If sum of distances of a point from the origin and lines \(x = 2\) is 4, then its locus is....