Match the circle equations in general form with their corresponding equations in standard form.Tilesx2 + y2 − 4x + 12y − 20 = 0(x − 6)2 + (y − 4)2 = 56x2 + y2 + 6x − 8y − 10 = 0 (x − 2)2 + (y + 6)2 = 603x2 + 3y2 + 12x + 18y − 15 = 0(x + 2)2 + (y + 3)2 = 185x2 + 5y2 − 10x + 20y − 30 = 0(x + 1)2 + (y − 6)2 = 462x2 + 2y2 − 24x − 16y − 8 = 0x2 + y2 + 2x − 12y − 9 = 0

1. [tex] x^2 + y^2 - 4x + 12y - 20 = 0 [/tex].

[tex] 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 [/tex] Answer B.

2. [tex] x^2 + y^2 +6x -8y - 10 = 0 [/tex].

[tex] 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 [/tex]

3. [tex] 3x^2 + 3y^2 +12x + 18y - 15 = 0 [/tex]. Divide by 3:

[tex] 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 [/tex] Answer C.

4. [tex] 5x^2 + 5y^2 -10x +20y - 30 = 0 [/tex]. Divide by 5:

[tex] 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 [/tex]

5. [tex] 2x^2 + 2y^2-24x -16y - 8 = 0 [/tex]. Divide by 2:

[tex] 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 [/tex] Answer A.

6. [tex] 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 [/tex] Answer D.