Question

Derive the equation of the parabola with a focus of (-5,-5) and a directrix of y=7.

Answer 1

Answer:

$y=-\frac{1}{24}(x+5)^2+1$

Step-by-step explanation:

The given parabola has its focus at (-5,-5) and the directrix is at: y=7.

The equation of such parabola is given by the formula:

$(x-h)^2=-4p(y-k)$

The vertex of the parabola is the midpoint of (-5,-5) and (-5,7).

$(\frac{-5+-5}{2},\frac{-5+7}{2} )=(-5,1)$

The value of p is the distance from the (-5,-5) to (-5,1).

p=|1--5|=6

We substitute the values of the vertex and p into the equation to get;

$(x--5)^2=-4(6)(y-1)$

$(x+5)^2=-24(y-1)$

Or

$y=-\frac{1}{24}(x+5)^2+1$