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

1 Answer
Dec 9, 2015

Answer:

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.