# How do you identify the following equation #25x^2 + 4y^2 = 100# as a circle, parabola, ellipse or hyperbola?

##### 1 Answer

Explanation below

- Ellipse,

#### Explanation:

The shape is

**Case 1) A parabola**, if only ONE variable is square

**Case 2) A circle**, if the coefficients of the variables are **addition** of the variables gives any number other than

**Case 3) An ellipse**, if the coefficients are anything other than **addition** of the variables gives

**Case 4) A hyperbola**, if both variables are squares, and **subtraction** of the variables gives

For this equation,

We have:

- Both variables are squares.
- The coefficients are other than
#1# .

We can divide both sides by

This satisfies Case 3 - It's an ellipse.