Find the center and the radius of the circle x^2+y^2+6x-4y-12=0 show your work

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

To obtain this form use the method of completing the square on both the x and y terms

rearranging

x² + 6x + y² - 4y = 12

x² + 2(3)x + 9 + y² + 2(- 2)y + 4 = 12 + 9 + 4

(x + 3)² + (y - 2)² = 25 ← in standard form

with centre = (- 3, 2) and r = = 5

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

3x + 4y -25 =0 represents the amount of change sianna should recieve