What is the equation of the circle in general form? x2+y2-6x+10y+25=0 x2+y2+6x-10y+25=0 x2+y2-6x+10y+22=0 x2+y2+6x-10y+22=0?

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Mathematics

25 March, 06:41

What is the equation of the circle in general form? x2+y2-6x+10y+25=0 x2+y2+6x-10y+25=0 x2+y2-6x+10y+22=0 x2+y2+6x-10y+22=0?

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Rachael Hernandez · Answer 1

By completing squares for all the equations we have:

x2 + y2-6x + 10y + 25 = 0

x2 + y2-6x + 10y = - 25

x2 + y2-6x + 10y + ( - 6/2) ^ 2 + (10/2) ^ 2 = - 25 + ( - 6/2) ^ 2 + (10/2) ^ 2

x2 + y2-6x + 10y + 9 + 25 = - 25 + 9 + 25

x2-6x + 9 + y2 + 10y + 25 = 9

(x-3) ^ 2 + (y + 5) ^ 2 = 9

x2 + y2 + 6x-10y + 25 = 0

x2 + y2 + 6x-10y = - 25

x2 + y2 + 6x-10y + (6/2) ^ 2 + ( - 10/2) ^ 2 = - 25 + (6/2) ^ 2 + ( - 10/2) ^ 2

x2 + y2 + 6x-10y + 9 + 25 = - 25 + 9 + 25

x2 + 6x + 9 + y2-10y + 25 = 9

(x + 3) ^ 2 + (y-5) ^ 2 = 9

x2 + y2-6x + 10y + 22 = 0

x2 + y2-6x + 10y = - 22

x2 + y2-6x + 10y + ( - 6/2) ^ 2 + (10/2) ^ 2 = - 22 + ( - 6/2) ^ 2 + (10/2) ^ 2

x2 + y2-6x + 10y + 9 + 25 = - 22 + 9 + 25

x2-6x + 9 + y2 + 10y + 25 = 12

(x-3) ^ 2 + (y + 5) ^ 2 = 12

x2 + y2 + 6x-10y + 22 = 0

x2 + y2 + 6x-10y = - 22

x2 + y2 + 6x-10y + (6/2) ^ 2 + ( - 10/2) ^ 2 = - 22 + (6/2) ^ 2 + ( - 10/2) ^ 2

x2 + y2 + 6x-10y + 9 + 25 = - 22 + 9 + 25

x2 + 6x + 9 + y2-10y + 25 = 12

(x + 3) ^ 2 + (y-5) ^ 2 = 12