Question

If the latus rectum of the ellipse \[ \frac{x^2}{16}+\frac{y^2}{b^2}=1 \] subtends an angle \[ \frac{\pi}{3} \] at the centre of the ellipse, then \(b^2=\)

• A. \(9\)
• B. \(\dfrac94(\sqrt{13}-1)\)
• C. \(\dfrac83(\sqrt{13}-1)\)
• D. \(7\)

Hint:

For an ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \] the endpoints of the latus rectum are \[ \boxed{\left(ae,\pm\frac{b^2}{a}\right)}. \] Use the angle made by the position vectors from the centre.

Answer 1

The Correct Option is C