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 $\sqrt{196} = 14$