Question

Using a directrix of y = −3 and a focus of (2, 1), what quadratic function is created

Answer 1

Distance from a point (x,y) on the graph of the function from the focus = distance from this point to the directrix. So we have

sqrt [( y-1^2 + (x - 2)^2] = y - (-3)

(y - 1)^2 + (x - 2)^2 = (y + 3)^2

y^2 - 2y + 1 + x^2 - 4x + 4 = y^2 + 6y + 9

8y = x^2 - 4x - 4

y = x^2/7 - x/2 - 1/2 Answer

Answer 2

5x+3 or (5,3) I think so