If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x --…

Question

If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x -- a2) = 0 and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

Accepted Answer

Vertex is (a2, 0)

y2 $=$ -(x - a2)  and  x $=$ 0 $$ \Rightarrow $$  (0, $$ \pm $$ 2a)

Area of triangle is $$ = {1 \over 2}.$$4a.(a2) = 250

$$ \Rightarrow $$  a3 = 125   or  a = 5

Solutions · 1