The product of the lengths of the perpendiculars drawn from the two foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ to the tangent at any point on the ellipse is

• A

  $6$
• B

  $7$
• C

  $8$
• Correct answer
  D

  $9$

Solution

(1) Product of length of perpendicular from focii to a tangent of ellipse $=(\text { semi minor axis })^2$
$\therefore \quad$ For $\frac{x^2}{9}+\frac{y^2}{25}=1$ Semi minor axis $=3$ $\therefore \quad$ Product of lengths of perpendiculars $=9$.

Hence, the correct answer is option: 'D'.