Question

What is the focus of a parabola with equation y^2=4x

Answer 1

Vertex: (0,0)(0,0)Focus: (1,0)(1,0)Axis of Symmetry: y=0y=0Directrix: x=−1

Answer 2

Focus = (1,0)

Explanation:

The equation of parabola with vertex at origin is given by:

`y^2 = 4ax` ....[1]

where, 4a is the width of the parabola and a is positive.

Focus = (a, 0)

Given the equation:

`y^2=4x` on comparing with [1] we have;

4a = 4

Divide both sides by 4 we have;

a = 1

Focus = (1, 0)

Therefore, the focus of a parabola with equation is, (1, 0)