Mathematics, 28.01.2020 04:31 BabyDino9415

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.

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The equation of the circle is $x^{2} + y^{2} +8x+12y+27=0$

we take x-es and y-s 'close' to each other, and complete the square:

$x^{2}+8x + y^{2} +12y+27=0$

write the coefficients of the linear terms (the x and y with degree 1) as 2*'something', to see how to complete the square:

$x^{2}+2*4*x + y^{2} +2*6*y+27=0$

which means that $x^{2}+2*4*x$ needs $4^{2}$

and $y^{2} +2*6*y$ needs $6^{2}$ to become perfect square trinomials:

$(x^{2}+2*4*x + 4^{2})-4^{2} + (y^{2} +2*6*y+ 6^{2})-6^{2} +27=0$

$(x+4)^{2}+ (y+6)^{2}=16+36-27$
$(x+4)^{2}+ (y+6)^{2}=25$

$(x-(-4))^{2}+ (y-(-6))^{2}= 5^{2}$

$(x-(-4))^{2}+ (y-(-6))^{2}= 5^{2}$

Answer from: genyjoannerubiera

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 from: Quest

(4,5

look up a corrdinate plane and do what the thingy says and boom

Answer from: Quest

yes

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8. 4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

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