From the point $P\left(\mathrm{3,4}\right)$ pair of tangents $PA$ and $PB$ are drawn to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1.$ If $AB$ intersects $y$-axis at $C$ and $x$-axis at $D$, then $OC·OD$ is equal to (where $O$ is the origin)

• A

  $9$
• B

  $18$
• C

  $8$
• Correct answer
  D

  $12$

Solution

Equation of the chord of contact of the tangents from point $P$ to the given ellipse is $\frac{3x}{16}+\frac{4y}{9}=1$
$\therefore C\left(0,\frac{9}{4}\right), D\left(\frac{16}{3},0\right)$

$\Rightarrow OC\times OD=\frac{9}{4}\times \frac{16}{3}=12$

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