Ois the origin & also the centre of two ...

`O`is the origin & also the centre of two concentric circles having radii of the inner & the outer circle as `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.

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