Question

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

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

Answer 1

Answer: (D)

$8\sqrt{2}$

The length of the latus rectum of any parabola $=4\times$ the distance between the latus-rectum and the tangent at the vertex.

Now the distance between the latus-rectum and the tangent at the vertex is $\frac{12-8}{\sqrt{1^2+1^2}}=2\sqrt{2}$ units.

So, length of the latus-rectum $=4\times 2\sqrt{2}=8\sqrt{2}$ units.