Question

Identify the correct statement(s) -

• A. the equation of the director circle of the ellipse, $5 x^2+9 y^2=45$ is $x^2+y^2=14$.
• B. the sum of the focal distances of the point $(0,6)$ on the ellipse $\frac{x^2}{25}+\frac{y^2}{36}=1$ is 10 .
• C. the point of intersection of any tangent to a parabola \& the perpendicular to it from the focus lies on directrix.
• D. all of these

Answer 1

Answer: (A)

(1) Here $\frac{x^2}{9}+\frac{y^2}{5}=1$
$\therefore $ director circle is
(2) $ x ^2+ y ^2=9$ Here $b>a$
$\therefore SP + S _1 P =2 b =12$
(3) It is lies on tangent at vertex