The answer is (x - 7)² + (y + 3)² = 7 or x² + y² - 14x + 6y + 51 = 0. Solution: We know that the standard form for the equation of a circle with the center located at coordinates (a, b) and radius r can be expressed as (x - a)² + (y - b)² = r²
Substituting the given information into the expression, we now have the equation of the circle whose center is at (7, -3) and radius equal to square root of 7: (x - 7)² + (y + 3)² = (square root of 7)² (x - 7)² + (y + 3)² = 7
We can get the general form for the equation of the circle by expanding the equation of the standard form. (x - 7)² + (y + 3)² = 7 (x - 7)(x - 7) + (y + 3)(y + 3) = 7 x² -14x + 49 + y² +6y + 9 = 7 x² + y² - 14x + 6y + 51 = 0
