The graph in the xy- plane of the equation above is a circle. What are the coordinates of the center of the circle?

The correct answer is: (5, -3)

HINT: Reduce the given equation to Circle’s equation and hence find the center of the circle.
Complete step by step Solution
Let’s apply the Completing square method, i. e take half of the coefficient of x term and y term from the given equation and square it. Then add it to the equation.
The coefficient of x - term is -10 and its half is -5. The square of -5 is 25.
Likewise, the coefficient of y - term is 6 and half of it is 3. The square of 3 is 9.
Let’s add these numbers, 25 and 9 on both LHS and RHS to balance the given equation.
Now, we get,
can be written as
We know that the circle’s equation is where, is the radius, and are and coordinates of the center of the circle respectively.
However, on comparing the Circle’s equation with the simplified equation, it is evident that h = 5 and k = - 3.
Hence, center of circle (h, k) = (5,-3)
So, the correct Option is C.