Find the eccentric angles of the extremities of the latus rectum of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1`

Options

A. `tan^(-1) (+- (ae)/(b))`
B. `tan^(-1) (+- (ae)/(a))`
C. `tan^(-1) (+- (b)/(ae))`
D. `tan^(-1) (+- (a)/(ae))`

Answer

C

Explanation

the coordinates of any point on the ellipse `(x^(2))/(a^(2))+(Y^(2))/(b^(2))=1` whose eccentric angle is `theta ` are ( `a cos theta , b sin theta`) the coordinates of the end points of latusrecta are `(ae ,+- (b^(2))/(a)))`.
`therefore a cos theta =ae and b sin theta=+-(b^(2))/(a)`
` implies tan theta =+- (b)/(ae)implies theta = tan ^(-1) (+-(b)/(ae))`