The equation of an ellipse is given by 5 x 2 + 5 y 2 − 6 x y − 8 = 0 . If r 1 , r 2 are distances of points on the ellipse which are at maximum \& minimum distance from origin then r 1 + r 2 =

Question

The equation of an ellipse is given by 5 x 2 + 5 y 2 − 6 x y − 8 = 0 . If r 1 ​ , r 2 ​ are distances of points on the ellipse which are at maximum \& minimum distance from origin then r 1 ​ + r 2 ​ =

TestHub · Accepted Answer

Any point on ellipse at a distance r from origin is ( $r cos θ, r sin θ$ )

$\Rightarrow r^{2} = \frac{8}{5 - 3 s i n 2 θ}$ is maximum if $5 - 3 sin 2 θ$ is minimum

$\Rightarrow r^{2} = 4$ $r^{2} m$ in if $(5 - 3 sin 2 θ)$ is maximum $= 8 \Rightarrow r^{2} = 1$

$r_{1} + r_{2} = 2 + 1 = 3$

Mathematics - Ellipse Question with Solution | TestHub

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