# Equation of a parabola Given Focus and Directrix

• May 20th 2008, 12:32 PM
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
• May 20th 2008, 01:20 PM
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.
• May 20th 2008, 02:36 PM
Quote:

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?
• May 20th 2008, 04:27 PM
topsquark
Quote:

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