The equation of a given circle in general form is x2+ y2 − 8x + 12y + 27 = 0. write the equation in standard form, (x − h)2 + (y - k)2 = r2, by completing the squares in the equation. show your work in a table.

Step                                                                     Reason

x2 + y2 - 8x + 12y + 27 = 0                                 given

x2 - 8x + y2 + 12y = -27                                      Isolate the constant term

x2 - 8x + 16 + y2 + 12y + 36 = -27 + 16 + 36      Complete the square by adding                              .                                                                           16 and 36 to both sides.

(x2 - 2∙4∙x + 42) + y2 + 12y + 36 = 25                Group and rearrange terms in x.

(x - 4)2 + y2 + 12y + 36 = 25                              (a - b)2 = a2 - 2ab + b2

(x - 4)2 + (y2 + 2∙6∙y + 62) = 25                         Group and rearrange terms in y.

(x - 4)2 + (y + 6)2 = 25                                        (a + b)2 = a2 + 2ab + b2

(x - 4)2 + (y + 6)2 = 52                                        Take the square root to find r = 5.

Step-by-step explanation:

this is the exact answer from plato

hope this helps a little bit :))

answer:  

123455421

step-by-step explanation: easy

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.