Question

What is the directrix of the parabola with the equation y+3=1/10(x+2)squared?

Answer 1

I am getting the line y = -11/2. But don't quote me on it.

Answer 2

Can you test the answer to see it's incorrect? Or do you have a choice of answers?

Answer 3

Possible answers are x=-3, y=-0.5, y=-5.5, and x=-2

Answer 4

Ok, well -11/2 is -5.5 So it's y = -5.5

Answer 5

Do you want to know how I got it?

Answer 6

Than you very much. Yes please

Answer 7

Ok, the equation that you gave us can be rewritten to get rid of the 1/10 fraction. Do that by multiplying the 10 by both sides to get this:\[10(y+3)=(x+2)^{2}\]On the right side the 10 and the 1/10 cancel each other out. I didn't show that step; it's understood (?)

Answer 8

Thank you

Answer 9

Now distribute the 10 into the parenthesis to get 10y + 30. Now the equation for finding the directrix and the focus is x^2 = 4py, where 10, the coefficient, is y. So 4p=10 and solve for p. P gives you 10/4=5/2. But since the center is at (-2,-3) and this is an x^2 parabola, the focus lies on the line of symmetry and the directrix is a y = line the same distance from the vertex as is the focus. The focus is 5/2 above the center of (-2,-3) and the directrix is 5/2 below the center of x=-2. It looks like this: