The focus of a parabola is (−3,−4) . The directrix of the parabola is y=1 .

What is the equation of the parabola?

y=−1 /10 (x−3/2)^2+3

y=−1/20(x−3/2)^2−3

y=−1/20(x+3)^2+3/2

y=−1/10(x+3)^2−3/2

jjennylove Feb 6, 2019

#1**+1 **

The directrix lies above the focus.....so...this parabola opens downward

To find the vertex ....we have ( -3, (-4 + 1)/2 ) = (-3, -3/2) = (h, k)

The distance from the vertex to the focus = p = l -4 - (-3/2) l = l -4 + 3/2l = l -8/2 + 3/2] = l -5/2l = 5/2

We have the following form

4p ( y - k) = - (x - h)^2 fill in what we know

4(5/2) (y - (-3/2) ) = - ( x - -3)^2 simplify

10 ( y + 3/2 ) = - ( x + 3)^2 divide both sides by 10

y + 3/2 = - (1/10) ( x + 3)^2 subtract 3/2 from both sides

y = - (1 /10) ( x + 3)^2 - 3/2

CPhill Feb 6, 2019