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 :))

the answe i =−n+5

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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