Question

Example 1

The following is the equation of a circle with radius 5 and center (1,2). Do you see why?
x^2−2x+1+y^2−4y+4=25

Answer 1

The answer to your question is getting the center and the radius of the polynomial we conclude that the data given are correct.

Explanation:

x² - 2x + 1 + y² - 4y + 4 = 25

First, factor the first three terms as a perfect square trinomial

(x - 1)² + y² - 4y + 4 = 25

Second, factor the last terms as a perfect square trinomial

(x - 1)² + (y - 2)² = 25

Get the numbers of each factor and change their signs

Ex (x -1)² = 1

(y - 2)² = 2

These numbers are the center of the circle (1, 2)

Get the square root of 25

`√(25) = 5` This is the radius

Then center = (1, 2) and radius = 5