Answer:
B)
Focus = (6,6), directrix is y = 4
Step-by-step explanation:
A parabola is the locus of a point that is equidistant from a fixed line (known as directrix) and a fixed point (known as focus).
The equation of a parabola in vertex form is given as:
[tex]y=a(x-h)^2+k[/tex]
It can be further simplified to:
[tex](x-h)^2=4p(y-k)[/tex]
The directrix of this parabola is given at line y = k - p and the focus is at (h, k + p)
Given that:
[tex]y = \frac{1}{4}(x-6)^2+ 5 \\(y-5)=\frac{1}{4}(x-6)^2\\(x-6)^2=4(y-5)[/tex]
Comparing (x-6)² = 4(y-5) with (x-h)² = 4p(y-k), It can be gotten that h = 6, p =1 and k = 5
The directrix of this parabola is given at line y = k - p = 5 - 1 = 4 and the focus is at (h, k + p) = (6, 5+1) = (6, 6)
Focus = (6,6), directrix is y = 4
