Question

Find the center and radius of each of the following circles x²+y²+4x-6y=5​

Answer 1

Explanation:

To find the center and radius of the circle x²+y²+4x-6y=5, we need to complete the square for both variables:

x²+4x+y²-6y=5

(x²+4x+4) + (y²-6y+9) = 18

(x+2)² + (y-3)² = 18

Therefore, the center of the circle is (-2,3), and the radius is the square root of 18, or approximately 4.24.

Answer 2

To find the center and radius of the circle given by the equation x² + y² + 4x - 6y = 5, we can complete the square for both the x and y terms.

Rearranging the equation, we have:

x² + 4x + y² - 6y = 5

To complete the square for the x-terms, we add (4/2)² = 4 to both sides of the equation:

x² + 4x + 4 + y² - 6y = 5 + 4

Similarly, to complete the square for the y-terms, we add (-6/2)² = 9 to both sides of the equation:

x² + 4x + 4 + y² - 6y + 9 = 5 + 4 + 9

Simplifying, we get:

(x + 2)² + (y - 3)² = 18

Comparing this equation to the standard form of a circle equation (x - h)² + (y - k)² = r², we can see that the center of the circle is (-2, 3) and the radius is the square root of 18, which simplifies to approximately 4.2426.