Question

In an ellipse length of minor axis is $8$ and eccentricity is $\frac{\sqrt{5}}{3}$ . The length of major axis is

• A. $6$
• B. $12$
• C. $10$
• D. $16$

Answer 1

Answer: (B)

$12$

Equation of the ellipse is

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

Given: $2b=8$ $\Rightarrow b=4$

$b^2=a^2(1-e^2)$

$16=a^2(1-{\left(\frac{\sqrt{5}}{3}\right)}^2)$

$16=a^2(1-\frac{5}{9})$

$a^2\left(\frac{4}{9}\right)=16$

$a^2=36\Rightarrow a=6$

Length of the major axis $=2a$

$=2\times 6=12$