Question

A circle is defined by the equation x²+y²-6x+4y-3=0. By method of completing squares, express the circle equation in the form (x-h)²+(y-k)²=r²​

Answer 1

(x-3)²+(y+2)²=4

Explanation:

x²+y²-6x+4y-3=0
x²-6x+y²+4y=3

(x²-6x+9)+(y²+4y+4)=3+9+4

(x-3)²+(y+2)²=16
(x-3)²+(y+2)²=4

Answer 2

To express the given circle equation in the form of (x - h)² + (y - k)² = r², we need to "complete the square" for both x and y terms. First, let's group the x terms and y terms together:

x² - 6x + y² + 4y = 3

To complete the square for x, we need to add and subtract the square of half of the coefficient of x:

x² - 6x + 9 + y² + 4y = 3 + 9

(x - 3)² + y² + 4y = 12

To complete the square for y, we need to add and subtract the square of half of the coefficient of y:

(x - 3)² + (y + 2)² - 4 = 12

(x - 3)² + (y + 2)² = 16

Therefore, the equation of the given circle in the form of (x - h)² + (y - k)² = r² is:

(x - 3)² + (y + 2)² = 4²

where the center of the circle is at (3, -2) and the radius is 4.