Question

Decide whether or not the equation has a circle as its graph. If it does, give the center and the radius. If it does not, describe the graph. x² + y² - 8x + 4y = -19

a) It represents a circle with center (4, -2) and radius 5.
b) It represents a circle with center (-4, 2) and radius 5.
c) It represents a circle with center (4, -2) and radius √19.
d) It does not represent a circle; it is a different type of graph.

Answer 1

The equation represents a circle with center (4, -2) and radius √(40) or 2√10.

Step-by-step explanation:

The given equation is x² + y² - 8x + 4y = -19.

To determine whether this equation represents a circle, we need to put it in the standard form of a circle equation, which is (x - h)² + (y - k)² = r².

By completing the square, we can rewrite the equation as (x - 4)² + (y + 2)² = 40.

This equation represents a circle with center (4, -2) and radius √(40) or 2√10.