JEE Main2012MathematicsParabolaActual

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

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Correct answer

B. 8

Step-by-step solution

Given parabola is x ^2=8 y 4 a=8 a=2 To find: Area of A B C aligned & A=(-2 a, a)=(-4,2) & B=(2 a, a)=(4,2) & C =(0,0) aligned aligned & Area = 1 2 | array ccc -4 & 2 & 1 4 & 2 & 1 0 & 0 & 1 array | & = 1 2 [-4(2)-2(4)+1(0)] & = -16 2 =-8 8 sq. unit & ( area cannot be negative ) aligned

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