# Is the equation #13x² + 13y² - 26x + 52y = -78 # a line, parabola, ellipse, hyperbola, or circle?

##### 2 Answers

Jul 25, 2018

No - it contains no real points.

#### Explanation:

Given:

#13x^2+13y^2-26x+52y=-78#

First note that all of the coefficients are divisible by

#x^2+y^2-2x+4y=-6#

Adding

#x^2-2x+1+y^2+4y+4 = -1#

That is:

#(x-1)^2+(y+2)^2 = -1#

Note that this is always false for real values of

Jul 25, 2018

**Imaginary circle**

#### Explanation:

The given equation:

Above equation shows a circle with a radius **imaginary circle with unit radius.**