# Thread: Finding the equation of an ellipse

1. ## Finding the equation of an ellipse

I need help with expanding the equation of a central ellipse. I know that

PF1+PF2 = sum of focal radii

sqrt[(x-0)^2+(y+3)^2] + sqrt[(x-0)^2+(y-3)^2] = 10

How do I get rid of the radicals?

2. Originally Posted by sun95
I need help with expanding the equation of a central ellipse. I know that

PF1+PF2 = sum of focal radii

sqrt[(x-0)^2+(y+3)^2] + sqrt[(x-0)^2+(y-3)^2] = 10

How do I get rid of the radicals?
Move a radical to the right hand side. Square both sides. Simplify. Isolate the remaining radical. Square both sides again. Simplify. Finito.

3. $\displaystyle\sqrt{x^2+(y+3)^2}+\sqrt{x^2+(y-3)^2}=10$

square both sides.

$\displaystyle x^2+(y+3)^2+x^2+(y-3)^2+2\sqrt{[x^2+(y+3)^2][x^2+(y-3)^2]}=100$

$\displaystyle 2x^2+2y^2-82=-2\sqrt{[x^2+(y+3)^2][x^2+(y-3)^2]}$

$\displaystyle 4x^4+4y^4+8x^2y^2-328x^2-328y^2+6724=4[x^4+y^4+2x^2y^2+18x^2-18y^2+81]$

Notice many of the terms will cancel out upon further simplification. I'll leave you to do the rest.