Question

Show that y = ax² + bx + c, a ≠ 0 represents a parabola and find its vertex, focus, directrix and latus rectum.

Answer 1

We have

Therefore, the vertex (X = 0, Y= 0) is given by

(-b/2a, 4ac - b²/4a)

The focus ( X = 0,Y =1/4a) is given by

The directrix equation is given by

Y = -1/4a or y = 4ac - b²/4a - 1/4a

The latus rectum is given by

4(1/4a) = 1/a