Question

HELP ME Using the following equation, complete the square and find the center and radius of the circle:

x2 + y2 + 4x − 6y − 12 = 0

You must show all work and calculations to receive credit.

Answer 1

Answer:
`(-2,3)`,
`r=5\ \text{units}`

Explanation:

Given

the equation is
`x^2+y^2+4x-6y-12=0`

completing the square

`\Rightarrow (x^2+2* 2* x+4-4)+(y^2-2*3* y+9-9)-12=0\\\Rightarrow (x^2+2* 2* x+4)+(y^2-2*3* y+9)-12-4-9=0\\\Rightarrow (x+2)^2+(y-3)^2=25\\\Rightarrow (x+2)^2+(y-3)^2=5^2\\\Rightarrow (x-(-2))^2+(y-3)^2=5^2`

Thus, the center of the circle is
`(-2,3)` and radius is
`r=5\ \text{units}`