Question

STATEMENT-1 : The locus of moving point $(x,y)$ satisfying $\sqrt{(x-2{)}^2+y^2}+\sqrt{(x-2{)}^2+y^2}=4$ is ellipse.
STATEMENT-2 : Distance between $(-2,0)$ and $(2,0)$ is $4.$

• A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
• B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
• C. STATEMENT-1 is True, STATEMENT-2 is False
• D. STATEMENT-1 is False, STATEMENT-2 is True

Answer 1

The correct option is D STATEMENT-1 is False, STATEMENT-2 is True

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

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

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

$\Rightarrow (x-2{)}^2+y^2=4$, which is the equation of a circle.

So, statement 1 is incorrect.

On the other hand, the statement 2 is correct since the distance between $(-2,0)$ and $(2,0)$ is $4$