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<h2>Hello!</h2>
The answer is:
The center of the circle is located on the point (-9,-2) and the radius is 6 units.
<h2>Why?</h2>To solve the problem, we need to use the given equation which is in the general form.
We are given the circle:
We know that a circle can be written in the following form:
Where,
h is the x-coordinate of the center of the circle
k is the y-coordinate of the center of the circle
r is the radius of the circle.
So, to find the center and the radius, we need to perform the following steps:
- Moving the constant to the other side of the equation:
- Grouping the terms:
- Completing squares for both variables, we have:
We need to sum to each side of the equation the following term:
Where, b, for this case, will the coefficients for both terms that have linear variables (x and y)
So, the variable "x", we have:
Where,
Then,
So, we need to add the number 81 to each side of the circle equation.
Now, for the variable "y", we have:
Where,
So, we need to add the number 4 to each side of the circle equation.
Therefore, we have:
Then, factoring, we have that the expression will be:
- Writing the standard form of the circle:
Now, from the simplified expression (after factoring), we can find the equation of the circle in the standard form:
Is also equal to:
Where,
Hence, the center of the circle is located on the point (-9,-2) and the radius is 6 units.
Have a nice day!