Question

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

Answer 1

Explanation below
- Ellipse, `(x^2)/4 + (y^2)/25= 1`

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 `1`, both variables are squares, and addition of the variables gives any number other than `1`.

Case 3) An ellipse, if the coefficients are anything other than `1`, both variables are squares, and addition of the variables gives `1`.

Case 4) A hyperbola, if both variables are squares, and subtraction of the variables gives `1`.

For this equation, `25x^2 + 4y^2= 100`,

We have:

1. Both variables are squares.
2. The coefficients are other than `1`.

We can divide both sides by `100`, to get the equation equal to `1`:

`(25x^2)/(100) + (4y^2)/100 = 100/100`

`=> (x^2)/4 + (y^2)/25 = 1`

This satisfies Case 3 - It's an ellipse.