Question

The vertex and focus of a parabola are $(-2,2),(-6,6)$. Then its length of latus rectum is

• A. $8\sqrt{2}$
• B. $4\sqrt{2}$
• C. $16\sqrt{2}$
• D. $12\sqrt{2}$

Answer 1

The correct option is C $16\sqrt{2}$

Distance between focus and vertex

$\begin{array}{c}focus\left(-6,6\right),vertex\left(-2,2\right)\\ a=\sqrt{{\left(-6+2\right)}^2{\left(6-2\right)}^2}\\ a=\sqrt{16+16}=4\sqrt{2}\end{array}$

length latus vectum

$\begin{array}{c}=4a=4\times 2\sqrt{2}\\ =16\sqrt{2}\end{array}$