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?
$\displaystyle \displaystyle\sqrt{x^2+(y+3)^2}+\sqrt{x^2+(y-3)^2}=10$
square both sides.
$\displaystyle \displaystyle x^2+(y+3)^2+x^2+(y-3)^2+2\sqrt{[x^2+(y+3)^2][x^2+(y-3)^2]}=100$
$\displaystyle \displaystyle 2x^2+2y^2-82=-2\sqrt{[x^2+(y+3)^2][x^2+(y-3)^2]}$
$\displaystyle \displaystyle 4x^4+4y^4+8x^2y^2-328x^2-328y^2+6724=4[x^4+y^4+2x^2y^2+18x^2-18y^2+81]$
Notice many of the terms will cancel out upon further simplification. I'll leave you to do the rest.