Equation of a parabola Given Focus and Directrix

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May 20th 2008, 12:32 PM
Daddycakes

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
Daddycakes

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:

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

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