How do you classify #13x² + 13y² - 26x + 52y = -78#?
It has the form of a circumference, but it would have negative radius, so it represents no point in the plane.
First of all, note that we have, coefficients apart, two quadratic terms (
Also, we see that the coefficients of the quadratic terms are equal (they're both
Now we can complete the squares:
Which we can rewrite into
We know that a circumference with center
Our equation mimics this one, except for the fact that we have