Mathematics - Parabola Question with Solution | TestHub

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