Question

The parametric representation of a point on the ellipse whose foci are (3, 0) and $(-1,0)$ and eccentricity 2/3 is

• A. $(1+3cos\theta ,\sqrt{3}sin\theta )$
• B. $(1+3cos\theta ,5sin\theta )$
• C. $(1+3cos\theta ,1+\sqrt{5}sin\theta )$
• D. $(1+3cos\theta ,1+5sin\theta )$
• E. $(1+3cos\theta ,\sqrt{5}sin\theta )$

Answer 1

Answer: (E)

Given that, foci are (3, 0) and $(-1,0)$ and $e=\frac{2}{3}$
$\therefore$ $2ae=4$
$\Rightarrow$ $2\times a\times \frac{2}{3}=4\Rightarrow a=3$ Also, $e=\sqrt{1-\frac{b^2}{a^2}}\Rightarrow \frac{4}{9}=1-\frac{b^2}{9}$
$\Rightarrow$ $\frac{b^2}{9}=1-\frac{4}{9}=\frac{5}{9}\Rightarrow b=\sqrt{5}$
$\therefore$ Parametric representation of a point is
$(1+3\cos \theta ,\sqrt{5}\sin \theta ).$