Class 11

Math

Co-ordinate Geometry

Conic Sections

$O$is the origin & also the centre of two concentric circles having radii of the inner & the outer circle as \displaystyle{a}&{b} respectively. A line $OPQ$ is drawn to cut the inner circle in $P$ & the outer circle in $Q.PR$ is drawn parallel to the $y$-axis & $QR$ is drawn parallel to the $x$-axis. Prove that the locus of $R$ is an ellipse touching the two circles. If the focii of this ellipse lie on the inner circle, find the ratio of inner: outer radii & find also the eccentricity of the ellipse.