question_answer

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   JEE Main Online Paper (Held On 12 May 2012)

A) 2                                             

B)                        8

C)                        1                                             

D)                        4

Correct Answer: B

Solution :

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