# Thread: Parabolas, Circles, Ellipses & Hyperbolas

1. ## Parabolas, Circles, Ellipses & Hyperbolas

Hey everyone! I am in precalculus trig right now and it's been about 7 years since my last math course. Can someone please tell me what I did wrong (probably my algebra?) in solving for the focus for this parabola.

Given equation: x^2 + 4x + 2y +10 = 0

to change to standard form I got: (x-(-2))^2 = 4(-1)(-1/2y - 3/2)

Focus (-2, -5/2) but answer was wrong, should have been (-7/2). Can someone show me how to get this?

2. ## Re: Parabolas, Circles, Ellipses & Hyperbolas

Given equation: x^2 + 4x + 2y +10 = 0
The standard form is $(x - h)^2 = 4p (y - k)$, where the focus is $(h, k + p)$ and the directrix is $y = k - p$.

$x^2+4x+4 + 2y + 6 = 0$

$(x+2)^2 + 2(y + 3) = 0$

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

$h = -2$, $k = -3$, $4p = -2 \implies p = -\dfrac{1}{2}$

vertex at $(-2,-3)$, focus at $\left(-2,-\dfrac{7}{2}\right)$