Need help: Let (x_0, y_0) be center of symmetry of Ax^2+By^2+Cx+Dy+F=0. Find...

[loadingazhd]

Can someone help me to solve this?

Let (x₀, y₀) be the center of symmetry of the curve Ax² + By² + Cx + Dy + F = 0. Find x₀ + y₀ A=1, B=2, C=3, D=4, F=1

Possible answers

(1)–2.589 (2) –2.537 (3) –2.500 (4) –2.436 (5) –2.393.

Please help am going mad!

 

[Jedi Equester]

You should notice, this equation is nothing else then an ellipse. So use the normal form of an ellipse:

\(\displaystyle \left(\frac xa\right)^2 + \left(\frac yb\right)^2 = 1\)

 

[ksdhart]

What have you learned recently in your class about the center of symmetry of a curve? For instance, what is the definition of center of symmetry of a curve? Have you tried graphing the curve x² + 2y² + 3x + 4y + 1 = 0? What shape does it make? Does that narrow down an approximate region where the center of symmetry might be for that curve? The more complete you can be about what you've already tried, the better we can advise you going forward.