Question

What is the equation of a parabola with vertex (4,4) and focus (7,4)

Answer 1

Answer A. x=1/12(y-4)^2+4. Hope that helped. 

Answer 2

`x = (1)/(12)(y-4)^2+4`

Explanation:

The equation of parabola is given by:

`x =(1)/(4a)(y-h)^2+k`

where,

(h, k) is the vertex and focus =(h+a, k)

As per the statement:

a parabola with vertex (4,4) and focus (7,4)

then;

Vertex = (h, k) = (4, 4)

⇒h = k = 4

Focus = (h+a, k) = (7, 4)

⇒h+a = 7

⇒4+a = 7

Subtract 4 from both sides we have;

a = 3

Substitute the given values we have;

`x =(1)/(12)(y-4)^2+4`

Therefore, a parabola with vertex (4,4) and focus (7,4) is,
`x = (1)/(12)(y-4)^2+4`