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If the area of the triangle whose one ve...

If the area of the triangle whose one vertex is at the vertex of the parabola, `y^(2) + 4 (x - a^(2)) = 0` and the other two vertices are the points of intersection of the parabola and Y-axis, is 250 sq units, then a value of 'a' is

A

`5 sqrt5`

B

5

C

`(10) ^(2//3)`

D

`5 (2 ^(1//3))`

Text Solution

Verified by Experts

The correct Answer is:
B
Parabola is `y ^(2) =-4 (x -a ^(2))`
`V (a ^(2) ,0),` let point of intersection of parabola with y-axis be A and B.Then `A (0,2a), B(0,-2a)`
`Delta =1/2|{:(a ^(2), 0,1),(0, 2a, 1),(0, -2a,1):}|=250," " 4a ^(3) =500implies a =5.`
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