Question

The equation of a circle is x2 + 8x + y2 - 12y = 144. What are the coordinates of the center and the length of the radius of the circle?

Answer 1

Answer:

The centre is the point (-4,6).

The length of the radius is 14.

Step-by-step explanation:

The equation of a circle has the following format:

$(x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}$

In which r is the radius and the centre is the point $(x_{0}, y_{0})$

In this question:

We have to complete the squares, to place the equation in the general format:

So

$x^{2} + 8x + y^{2} - 12y = 144$

To complete the quares, we divide each first order term(8 and -12) by two, having two new terms(4 and -6). With this, we write as the square of (x+4) and (y-6). To compensate, we have to find the square of 4 and -6 on the other side of the equality.

$(x+4)^{2} + (y-6)^{2} = 144 + (4)^{2} + (-6)^{2}$

$(x+4)^{2} + (y-6)^{2} = 196$

The centre is the point (-4,6).

The length of the radius is $\sqrt{196} = 14$

Answer 2

The center and the length of the radius of the circle is (-4, 6) and 14units respectively

Equation of a circle

The standard equation of a circle is expressed as:

x^2+y^2+2gx+2fy+c = 0

where:

C = (-g, -f)

r = √g²+f²-c

Given the equation of a circle expressed as:

x^2 + 8x + y^2 - 12y = 144.

Compare both equations

2gx = 8x
g = 4

2fy = -12y

y = -6

The centre of the circle will be at (-4, 6)

Determine the radius

r = √4²+6²+144
r = 14

Hence the center and the length of the radius of the circle is (-4, 6) and 14units respectively

Learn more on the equation of a circle here: https://brainly.com/question/1506955