Question

How do you find the standard form given `x^2+y^2-6x+4y+14=0`?

Answer 1

Shown below

Explanation:

Complete the square on both `x` and `y`

`x^2 -6x + 9 + y^2 + 4y + 4 = -14 + 9 + 4`

`(x-3)^2 + ( y +2)^2 = -1`

`=> EE x , y in CC`

In other words when you try and sketch thus graph on a cartesian plane, nothing shows up, no real values of `x` and `y` satisfy this equation