Question

Which is the equation of a parabola with vertex (0,0), that opens to the right and has a focal width of 8?

Answer 1

Vertex: V=(0,0)=(h,k)→h=0, k=0

Opens downward:

(x-h)^2=4p(y-k)

Width focal: p=-6<0 (donwnward)

Replacing h=0, k=0 and p=-6 in the equation above:

(x-0)^2=4(-6)(y-0)

x^2=-24y

Answer: The equation of the parabola is x^2=-24y

Explanation:

Answer 2

Equation of parabola:

`y^2=8x`

Explanation:

A parabola with vertex (0,0), that opens to the right.

The general equation of parabola open right whose vertex (0,0)

`y^2=4px`

Focal width : Two points opposite to the the focus on parabola.

Distance between these two points is called focal width i,e 4p

Focal width = 8

So, 4p=8

p=2

Focus: (2,0)

Equation of parabola:

`y^2=8x`