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

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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?

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-02-23T23:08:40+03:00

Answer:

The center of the circle is at the coordinates (-4,6).

The radius measures 14 units.

Step-by-step explanation:

The general formula for a circle is as follows:

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

Where r denotes the radius and the center is specified at $(x_{0}, y_{0})$

Specifics for this question:

We need to complete the squares to convert the equation into its standard format:

So

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

To complete the squares, each first degree term (8 and -12) is divided by two, yielding new terms (4 and -6). This allows us to express it as the square of (x+4) and (y-6). To balance the equation, we must incorporate the squares of 4 and -6 on the opposite side.

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

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

The center is located at the coordinates (-4,6).

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