Question

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

Answer 1

Answer:

radius = 2

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

Given

x² + y² + 8x - 6y + 21 = 0

Use the method of completing the square to obtain standard form

Collect the x- terms and y- terms together and subtract 21 from both sides

x² + 8x + y² - 6y = - 21

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(4)x + 16 + y² + 2(- 3)y + 9 = - 21 + 16 + 9

(x + 4)² + (y - 3)² = 4 ← in standard form

with centre (- 4, 3) and radius = $\sqrt{4}$ = 2

Answer 2

Answer:

2

Step-by-step explanation:

Center: (−4,3)

Radius: 2