Question

What is the equation of the quadratic graph with a focus of (2, 0) and a directrix of y = −12?

Answer 1

f(x)=
`(1)/(24) x^2-(1)/(6)x-(35)/(6) \\` I just took the test and it is right

Explanation:

Answer 2

distance from the point (x,y) to the focus = distance of (x,y) from the directrix
so we have

sqrt [(x - 2)^2 + y2] = 12 + y

squaring both sides
x^2 - 4x + 4 + y^2 = 144 + 24y + y^2

x^2 - 4x + 4 = 144 + 24y

24y = x^2 -4x - 140

y = x^2/24 - x/6 - 35/6 is the required equation