Question

regan is trying to find the equation of a quadratic that has a focus of (-2,5) and a directrix of y = 13 describe to regan your preferred method for deriving the equation. Make sure you use regans situation as a model to help her understand

Answer 1

AS the directrix y = 13 is horizontal the equation of the quadratic opens upwards or downwards. The graph is also called a parabola.

For a parabola the distance of any point on the curve to the directrix = the distance from that point to the focus.

So for any point (x, y) distance from the focus is sqrt(; x - -2)^2 + (y - 5)^2 and the distance from the point to the directrix is |y - 13|

So sqrt [ (x + 2)^2 + (y - 5)^2] = |y - 13|

Simplifying will give us the equation of the parabola.