What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 units?

Solution:

The general form of the equation of the circle is:

(x - h)² + (y - k)² = a² ---->(1)

Where (h, k) is the coordinates of the center of the circle and a is the radius.

The given equation can be rewritten in the standard form as follows:

x²+ y² + 8x - 6y + 21 = 0

x² + 8x + y² - 6y = -21

Adding 16 and 9 on both sides of the equation, by completing the square, we get

x² + 8x + 16 + y² - 6y + 9 = -21 + 16 + 9

(x + 4)² + (y - 3)² = 4

(x + 4)² + (y - 3)² = 2²---->(2)

By comparing equations (1) & (2) we can conclude that the center of the circle is (-4, 3) and the radius is 2 units.

What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 units?

Summary:

The problem statement requires finding the radius of the circle of the equation x² + y² + 8x - 6y + 21 = 0 units. The radius calculated is 2 units.