The general form of the equation of a circle is x2+y2−4x−8y−5=0.What are the coordinates of the center of the circle?Enter your answer in the boxes.( , )
Accepted Solution
A:
Know that the equation for a circle is: (x - h)² + (y - k)² = r²
where (h, k) is the coordinate for the center and r = radius
Factor into a perfect square for x and y by adding/subtracting grouping constants.
Given equation: x² + y² - 4x - 8y - 5 = 0
going to group all x terms together and add +4 to both sides to give a perfect square of x. This number is determined by taking the square of half the middle term coefficient. [-4x is middle term. (-4/2)² = 4]