Question

What is the length of latusrectum of the ellipse $16x^2+y^2=16?$

Answer 1

Given ellipse is $16x^2+y^2=16?$

On dividing both sides we get

$\frac{x^2}{1}+\frac{y^2}{16}=1$ On comparing this equation with the standard equation of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , we get

$a^2=1,and{b}^2=16\Rightarrow a=1andb=4$

Here, b>a

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