Question

A certain circle can be represented by the following equation x2+y2+12x+4y+15=0

Answer 1

Answer:

(-6, -2)

radius = 5 units

Step-by-step explanation:

see attached for reference

recall that the general form for an equation of a circle looks something like:

x² + y² + Cx + Dy + E = 0, where

if (h,k) are the coordinates of the center of the circle,

h = - C/2   and k = -D/2

In our case, we are given:

x² + y² + 12x + 4y + 15 = 0

IF we compare this with the general equation above, we can see that

C = 12, D = 4 and E = 15

hence,

h = - C/2 = - (12/2) = -6

k = - D/2 = -4/2 = -2

Hence (h, k) = (-6, -2)

also, the radius is given by the equation

r² = (1/4)(C² + D²) - E

= (1/4)(12²+4²) - 15

= 40-15

= 25

r = ±√25

= ±5   (ignore negative because radius is always positive)

= 5