Question

The area (in sq.units) of a triangle formed by joining the vertex and the endpoints of the latus rectum of the parabola \(x^{2}=-20y\) is...

• A. \(100\)
• B. \(200\)
• C. \(50\)
• D. \(10\)

Hint:

Find the endpoints of the latus rectum, then use base times height over two.

Answer 1

The Correct Option is C

Step 1: Formula
The latus rectum has length $4a=20$ and is at distance $a=5$ from the vertex.

Step 2: Area
Area $=\frac{1}{2}\times 4a\times a=2a^2$.

Step 3: Substitute
$2\times 25=50$, the third option.

Final Answer:
The area is 50 square units. \[ \boxed{\text{(C) }50} \]