Question

What is the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = −10 ?

Answer 1

These are the options i dont really understand what to do.
f(x) = −one twentieth (x − 6)2 + 5
f(x) = −one twentieth (x − 6)2 − 5
f(x) = one twentieth (x − 6)2 + 5
f(x) = one twentieth (x − 6)2 − 5

Answer 2

The graph will be a parabola.
Parabola has this property where any point (x,y) on the parabola will be equidistant from the focus and the directrix. Therefore,
(x-6)^2 + (y-0)^2 = (y - -10)^2
(x-6)^2 + y^2 = (y +10)^2
simplify

Answer 3

(x-6)^2 + y^2 = (y +10)^2
(x-6)^2 = (y +10)^2 - y^2
= (y+10+y)(y+10-y)
= (2y+10)(10)
= 2(y+5)(10)
= 20(y+5)
1/20*(x-6)^2 = y+5
y = 1/20*(x-6)^2 - 5

Answer 4

thank you!

Answer 5

you are welcome.