Question

Which graph represents the equation x2 = 8y?

Answer 1

Answer:

Given Equation : x² = 8y

Given Equation matches with standard equation of parabola on positive y-axis

x² = 4ay

By comparing both equation we get,

4a = 8 ⇒ a = 2

Focus of parabola = ( 0 , 2 )

Vertex of parabola = ( 0 , 0 )

Axis of Symmetry = y-axis

To draw its, we find some points

when x = 4 or -4 we get

4² = 8y ⇒ 16 = 8y ⇒ y = 2

So, points are ( 4 , 2 ) and  ( -4 , 2 )

when x = 8 or -8 we get

(-8)² = 8y ⇒ 64 = 8y ⇒ y = 8

So, points are ( 8 , 8 ) and ( -8 , 8 )

Graph from above points is attached.

Answer 2

Direction: Opens up
Vertex: (0,0)
Focus: (0,2)
Axis of Symmetry: x=0
Directrix: y=-2