Question

The equation of the latus rectum of a parabola is $x+y=8$ and the equation of the tangent at the vertex is $x+y=12$. Then the length of the latus rectum is

• A. $4\sqrt{2}\text{units}$
• B. $2\sqrt{2}\text{units}$
• C. $8\text{units}$
• D. $8\sqrt{2}\text{units}$

Answer 1

The correct option is D $8\sqrt{2}\text{units}$

Since, $x+y=8$ and $x+y=12$ are parallel.
Therefore, distance between them is,
$AS=\left|\frac{C_1-C_2}{\sqrt{a^2+b^2}}\right|=\frac{4}{\sqrt{2}}=2\sqrt{2}$

Hence, length of the latus rectum is,
$LR=4AS$
$=4\times 2\sqrt{2}$
$=8\sqrt{2}\text{units}$