Statement-I: Any chord of the ellipse x2+y2+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.

Question

Statement-I: Any chord of the ellipse x2+y2+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.

Tardigrade Admin · Accepted Answer

x2+y2+x y=1 Replacing x by - x y by - y we get the same equation. ∴ 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.

Q. 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.

Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.

Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I.

Statement-I is true, Statement-II is false.

Statement-I is false, Statement-II is true.

$x^{2} + y^{2} + x y = 1$
Replacing $x$ by $- x & y$ by $- y$ we get the same equation.
$∴$ 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.

Q. Statement-I : Any chord of the ellipse x2+y2+xy=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.