Question

Can you help me with these two questions please !!!!

Answer 1

1) Choice B

(x-2)^2 + (y+4)^2 = 16

2) Choice A

(x-6)^2 + (y+4)^2 = 20

Explanation:

Equation for circle is (x-h)^2 + (y-k)^2 = r^2

(h,k) is cords

1) (x-2)^2 + (y+4)^2 = 16

Cords = (-2, 4)

radius =
`√(16)` = 4

2) x^2 + y^2 - 12x +8y +32 = 0

x^2 - 12x + y^2 +8y +32 = 0

Choice A

(x-6)^2 + (y+4)^2 = 20

Multiply it out

x^2 - 12x + 36 + y^2 +8y + 16 = 20

Combine same values

x^2 - 12x + y^2 +8y + 52 = 20

Bring it all to one side (subtract)

x^2 - 12x + y^2 +8y +32 = 0

Answer 2

Answer:
`(x+2)^(2)+(y-4)^(2) =16`

and

`(x-6)^(2) +(y+4)^(2) =20`

Explanation:

Equation for a Circle

`(x-h)^(2) +(y-k)^(2) =r^(2)`

h= -2 k= 4 r= 4

`(x+2)^(2)+(y-4)^(2) =16`

Part 2

Complete the Square

`x^(2) +y^(2) -12x+8y+32=0\\(x^(2)-12x+-)+(y^(2)+8y)=-32\\(x^(2) -12x+36)=(y^(2) +8y+16)=-32+36+16\\\\(x-6)^(2) +(y+4)^(2) =20`