Needing some help with ellipses....

[pidgezero_one]

Does anyone know how to calculate the equation of an ellipse (in this case, (x^2/b^2) + (y^2/a^2) = 1) when the only given information is that the center is (0,0) and that 2 points on the ellipse are (2, -2) and (-2/3, 10/3)?

Any help would be greatly appreciated. Sorry if this is in the wrong forum, the education system where I live covers different things at different levels than in other places. I'm in Grade 11. @__@;

 

[galactus]

Substitute (-2,2) and (-2/3,10/3) into the ellipse equation to get:

\(\displaystyle \L\\\frac{4}{A}+\frac{4}{B}=1\) and \(\displaystyle \L\\\frac{4}{9A}+\frac{100}{9B}=1\)

Solve first equation for A:

\(\displaystyle \L\\B4+A4=AB\)

\(\displaystyle 4B=AB-A4\)

\(\displaystyle 4B=A(B-4)\)

\(\displaystyle A=\frac{4B}{B-4}\)

Now, sub that into the second equation and solve for B. You'll then have your A and B to fill in your ellipse equation.

 

[pidgezero_one]

I got it! Thank you for your help!