Question

Locus of the point whose sum of distances from the origin and the $x-$ axis is $4$ units is

• A. $x^2=8(2-y),y\ge 0$
• B. $x^2=8(2+y),y\ge 0$
• C. $x^2=8(2+y),y<0$
• D. $x^2=8(2-y),y<0$

Answer 1

Answer: (A), (C)

The correct options are
A $x^2=8(2-y),y\ge 0$
C $x^2=8(2+y),y<0$

Let $P(x,y)$ be a point which satisfies the given condition
$\sqrt{x^2+y^2}+|y|=4$
when $y\ge 0$ then
$\sqrt{x^2+y^2}=4-y$
$\Rightarrow x^2+y^2=16-8y+y^2$
$\Rightarrow x^2=8(2-y)$
when $y<0$
$\sqrt{x^2+y^2}-y=4$
$\Rightarrow \sqrt{x^2+y^2}=4+y$
$\Rightarrow x^2+y^2=16+8y+y^2$
$\Rightarrow x^2=8(2+y)$