Question

Write the equation of a circle in standard form for the following:

Answer 1

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~~