Question

The product of the perpendiculars drawn from the foci of the ellipse, $\frac{x^2}{9}+\frac{y^2}{25}=1$ upon the tangent to it at the point $(\frac{3}{2},\frac{5\sqrt{3}}{2})$, is:

• A. $9$
• B. $\frac{189}{13}$
• C. $18$
• D. $3\sqrt{13}$

Answer 1

Answer: (A)

$9$

Comparing with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Her $a=3,b=5$

$b^2>a^2,$

$\therefore$ from the property of ellipse,

Product of lengths of perpendiculars drawn from focii of ellipse $=a^2$

So, product of lengths of perpendiculars $=9$

Correct option is A