Question

Which of the following is/are true?

• A. Equation of auxiliary circle of ellipse,
• B. Sum of focal distance of any point on the ellipse is a+b.
• C. For to be an ellipse a > b.
• D. In the parametric representation of point where P lies on ellipse , is the angle made by P with respect to major axis.

Answer 1

The correct option is A

Equation of auxiliary circle of ellipse,

Option (a) $\frac{x^2}{9}+\frac{y^2}{5}=1\Rightarrow a=3,b=\sqrt{5}\therefore \text{Equation of auxiliary circle is}{x}^2+y^2=3^2=9$
Option (b) Sum of distances of any point on ellipse to its foci is 2a.
Option (c) $\frac{{}^{x^2}}{a^2}+\frac{y^2}{b^2}=1$ can be ellipse for a $<$ b & a $>$ b and when a=b it is special case of circle.
Option (d) $\theta$ is angle made by $(acos\theta ,asin\theta )$ the point perpendicularly above P lying on the auxiliary circle.