Question

If the length of the major axis intercepted between the tangent and normal at a point `P (a cos theta, b sin theta)` on the ellipse `(x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1` is equal to the length of semi-major axis, then eccentricity of the ellipse is
A. `(cos theta)/(sqrt(1-cos theta))`
B. `(sqrt(1-cos theta))/(cos theta)`
C. `(sqrt(1-cos theta))/(sin theta)`
D. `(sin theta)/(sqrt(1-sin theta))`

Answer 1

Correct Answer - B
Tangent at point `P (a cos theta, b sin theta)` meets x-axis at `(a)/(cos theta)` Normal at point `P(a cos theta, b sin theta)` meets x-axis at `((a^(2)-b^(2)))/(a) cos theta`
According to the equation `(a)/(cos theta) - ((a^(2)-b^(2)))/(a) cos theta =a`
`rArr e^(2) cos^(2) theta =1 - cos theta rArr e = (sqrt(1-cos theta))/(cos theta)`