Question

If normal at any poin P on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0)` meets the major and minor axes at Q and R, respectively, so that 3PQ=2PR, then find the eccentricity of ellipse

Answer 1

Correct Answer - `(1)/(sqrt(3))`
Normal at point P meets the major axis minor axes at Q and R, respectively.
`:. (PQ)/(PR)=(b^(2))/(a^(2))`
Given `(PQ)/(PR)=(2)/(3)`
`:. (b^(2))/(a^(2))=(2)/(3)`
`:. E^(2)=1-(b^(2))/(a^(2))=1-(2)/(3)=(1)/(3)`
`rArre=(1)/(sqrt(3))`