Answer:
[tex]x = \frac{1}{12}(y-4)^2+4[/tex]
Step-by-step explanation:
The equation of parabola is given by:
[tex]x =\frac{1}{4a}(y-h)^2+k[/tex]
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;
[tex]x =\frac{1}{12}(y-4)^2+4[/tex]
Therefore, a parabola with vertex (4,4) and focus (7,4) is, [tex]x = \frac{1}{12}(y-4)^2+4[/tex]
