To determine the center of the circle;
x² + y² - 14x - 10 y - 26 = 0
we have to make the above equation to be in the form;
(x-a)² + (x-b)² = r²
where (a,b) is the center of the circle and r is the radius of the circle
x² + y² - 14x - 10 y - 26 = 0
add 26 to both-side of the equation
x² + y² - 14x - 10 y - 26 + 26 = 0 + 26
x² + y² - 14x - 10 y = 26
x² - 14x +y² - 10y = 26
add square of half of each coefficient
x² - 14x + (-7)² + y² -10y + (-5)² = 26 + (-7)² + (-5)²
(x -7)² + (y-5)² =
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