Question

The following are the standard equation of a circle with center at the origin and radius of 2, except: a. x^2-4=-y^2b. x^2+4=-y^2c. x^2+y^2=2^2d. x^2+y^2=4

Answer 1

The equation of a circle is defined as

`\begin{gathered} x^2+y^2=r^2 \\ \text{where} \\ r\text{ is the radius} \end{gathered}`

Given that the radius of the circle is 2, then the equation of the circle is

`x^2+y^2=2^2\text{ (option C)}`

Which can then be simplified to

`x^2+y^2=4\text{ (option D)}`

And we can rearrange the equation

`x^2-4=-y^2\text{ (option A)}`

Which means that it cannot be the equation

`x^2+4=-y^2`