How do you identify the following equation #25x^2 + 4y^2 = 100# as a circle, parabola, ellipse or hyperbola?
The shape is
Case 1) A parabola, if only ONE variable is square
Case 2) A circle, if the coefficients of the variables are
Case 3) An ellipse, if the coefficients are anything other than
Case 4) A hyperbola, if both variables are squares, and subtraction of the variables gives
For this equation,
- Both variables are squares.
- The coefficients are other than
We can divide both sides by
This satisfies Case 3 - It's an ellipse.