Question

The area of triangle formed by the lines joining the vertex of the parabola, $x^2=8y$, to the extremities of its latus rectum is

• A. 2
• B. 8
• C. 1
• D. 4

Answer 1

Answer: (B)

Given parabola is $x^2=8y$
$\Rightarrow 4a=8\Rightarrow a=2$
To find: Area of $\Delta ABC$
$A=\left(-2a,a\right)=\left(-4,2\right)$
$B=\left(2a,a\right)=\left(4,2\right)$
$C=\left(0,0\right)$
$\therefore$ Area $=\frac{1}{2}\left|\begin{array}{ccc}-4& 2& 1\\ 4& 2& 1\\ 0& 0& 1\end{array}\right|$
$=\frac{1}{2}\left[-4\left(2\right)-2\left(4\right)+1\left(0\right)\right]$
$=\frac{-16}{2}=-8\approx 8sq.$ unit
($\because$ area cannot be negative)