# Thread: Equation of a parabola Given Focus and Directrix

1. ## Equation of a parabola Given Focus and Directrix

Need some help writting a formula for this conic section.

Given: Focus is (1,1) and directrix is y=-x-2

Thanks

2. You can use the distance formula and the formula for the distance from a point to a line.

$\sqrt{(x-1)^{2}+(x-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}$

Square both sides:

$2(x-1)^{2}=\left(\frac{x+y+2}{\sqrt{2}}\right)^{2}$

Expand and simplify.

3. Originally Posted by galactus
You can use the distance formula and the formula for the distance from a point to a line.

$\sqrt{(x-1)^{2}+(x-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}$

Square both sides:

$2(x-1)^{2}=\left(\frac{x+y+2}{\sqrt{2}}\right)^{2}$

Expand and simplify.
thanks. Anyone else?

4. Originally Posted by Daddycakes
thanks. Anyone else?
Anyone else for what? Show us what you have done after galactus' post. If you can't get any further than that point, let us know. Be specific!

-Dan

Edit: Actually a slight change is needed here:
$\sqrt{(x-1)^{2}+(x-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}$

should be
$\sqrt{(x-1)^{2}+(y-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}$

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

-Dan