Question

Match the circle equations in general form with their corresponding equations in standard form.

Tiles
x2 + y2 − 4x + 12y − 20 = 0
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 6x − 8y − 10 = 0
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
(x + 2)2 + (y + 3)2 = 18
5x2 + 5y2 − 10x + 20y − 30 = 0
(x + 1)2 + (y − 6)2 = 46
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 + 2x − 12y − 9 = 0

Answer 1

x2 + y2 − 4x + 12y − 20 = 0 and (x-2)2 + (y+6)2 = 60

x2 + y2 + 2x - 12y - 9 = 0 and (x + 1)2 + (y - 6)2 = 46

2x2 + 2y2 - 24x - 16y - 8 = 0 and (x - 6)2 + (y - 4)2 = 56

3x2 +3y2 + 12x +18y - 15 = 0 and (x + 2)2 + (y + 3)2 = 18

I got a 100 on PLATO

Explanation:

Answer 2

1.
`x^2 + y^2 - 4x + 12y - 20 = 0`.


`x^2-4x+4-4+y^2+12y+36-36-20=0,\\ (x-2)^2+(y+6)^2-60=0,\\ (x-2)^2+(y+6)^2=60` Answer B.

2.
`x^2 + y^2 +6x -8y - 10 = 0`.


`x^2+6x+9-9+y^2-8y+16-16-10=0,\\ (x+3)^2+(y-4)^2-35=0,\\ (x+3)^2+(y-4)^2=35`

3.
`3x^2 + 3y^2 +12x + 18y - 15 = 0`. Divide by 3:


`x^2+4x+4-4+y^2+6y+9-9-5=0,\\ (x+2)^2+(y+3)^2-18=0,\\ (x+2)^2+(y+3)^2=18` Answer C.

4.
`5x^2 + 5y^2 -10x +20y - 30 = 0`. Divide by 5:


`x^2-2x+1-1+y^2+4y+4-4-6=0,\\ (x+1)^2+(y+2)^2-11=0,\\ (x+1)^2+(y+2)^2=11`

5.
`2x^2 + 2y^2-24x -16y - 8 = 0`. Divide by 2:


`x^2-12x+36-36+y^2-8y+16-16-4=0,\\ (x-6)^2+(y-4)^2-56=0,\\ (x-6)^2+(y-4)^2=56` Answer A.

6.
`x^2 + y^2 + 2x-12y-9 = 0,\\ x^2+2x+1-1+y^2-12y+36-36-9=0,\\ (x+1)^2+(y-6)^2=46` Answer D.