Question

The equation of an ellipse is given in its standard form as $16x^2+y^2=16$, then the length of the latus rectum is,

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $4$
• D. $2$

Answer 1

The correct option is B $\frac{1}{2}$

Equation of ellipse given, $16x^2+y^2=16$

Dividing both sides by $16$

$\frac{x^2}{1}+\frac{y^2}{16}=1$

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

$a^2=1⟹a=1and{b}^2=16⟹b=4(b>a)$

$\therefore$ Length of the latus rectum $=\frac{2a^2}{b}=\frac{2\times 1}{4}=\frac{1}{2}$

Hence option ${}^{\prime }{B}^{\prime }$ is the answer.