Question

Statement-I : Any chord of the ellipse $x^2+y^2+x y=1$ through $(0,0)$ is bisected at $(0,0)$ Because
Statement-II : The centre of an ellipse is a point through which everv chord is bisected.

• A. Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
• B. Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I.
• C. Statement-I is true, Statement-II is false.
• D. Statement-I is false, Statement-II is true.

Answer 1

Answer: (A)

$x^2+y^2+x y=1$
Replacing $x$ by $- x \& y$ by $- y$ we get the same equation.
$\therefore$ Centre of conic is $(0,0)$ and every chord passing through the centre is bisected by the point. Hence st. I & st. II both are true & st I explains st. II.