Question

Select the correct answer.
A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the
A.
(-7, -1). 36 units
'B.
c.
D.
(7.1). 36 units
(7.1), 6 units
(-7, -1), 6 units
Next

Answer 1

Answer:

(- 7, - 1), 6 units

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - h)² = r²

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

Given

x² + y² + 14x + 2y + 14 = 0

Collect x/y terms together and subtract 14 from both sides

x² + 14x + y² + 2y = - 14

To obtain standard form use the method of completing the square

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

x² + 2(7)x + 49 + y² + 2(1)y + 1 = - 14 + 49 + 1

(x + 7)² + (y + 1)² = 36 ← in standard form

with centre (- 7, - 1) and radius = $\sqrt{36}$ = 6