Circle Equations
Write the equation of a circle in standard form for the following:
x² − 14x + 49 + y² + 4y = 0
To write the general form of a circle into standard form, use the formula
(x - h)² + (y - k)² = r²
Where,
(h, k) is the center; and
r is the radius
To transform general form to standard form, group the terms that has the same variables. Replace 0 with the constant term.
- x² - 14x + 49 + y² + 4y = 0
- (x² - 14x) + (y² + 4y) = -49
Next step is to complete the square of each equation inside the parentheses.
- (x² - 14x) + (y² + 4y) = -49
- (x² - 14x - 49) + (y² + 4y + 2) = -49 - 49 + 2
Then factor each equation inside the parentheses.
- (x² - 14x - 49) + (y² + 4y + 2) = -49 - 49 + 2
- (x - 7)² + (y + 2)² = √2
- (x - 7)² + (y + 2)² = 4
Answer:
- The standard form of the circle is (x - 7)² + (y + 2)² = 4.
Wxndy~~