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Karo-lina-s [1.5K]
3 years ago
7

The equation x2 + y2 − 2x + 2y − 1 = 0 is the general form of the equation of a circle. What is the standard form of the equatio

n?
Mathematics
2 answers:
Alla [95]3 years ago
8 0
X^2 + y^2 - 2x + 2y - 1 = 0

(x^2 - 2x) + (y^2 + 2y) - 1 = 0

(x^2 - 2x + 1) + (y^2 + 2y + 1) - 1 - 1 - 1 = 0

(x - 1)^2 + (y + 1)^2 - 3 = 0

(x - 1)^2 + (y + 1)^2 = 3


qaws [65]3 years ago
7 0

Answer:

(x-1)^2+ (y+1)^2=3

Step-by-step explanation:

x^2 + y^2 - 2x + 2y - 1 = 0

Standard form of the equation is (x-h)^2 + (y-k)^2= r^2

To get standard form we apply completing the square method

x^2-2x+ y^2+ 2y - 1 = 0

Take coefficient of x  and y . Divide it by 2 and then square it

\frac{2}{2} =1 and 1^2=1

Add and subtract 1

(x^2-2x)+(y^2+ 2y) - 1 = 0

(x^2-2x+1-1)+(y^2+ 2y+1-1) - 1 = 0

(x^2-2x+1)+(y^2+ 2y+1)-1-1- 1 = 0

(x^2-2x+1)+(y^2+ 2y+1)-3= 0

Now write the parenthesis in square form

(x-1)(x-1)+ (y+1)(y+1)-3= 0

(x-1)^2+ (y+1)^2-3= 0 , add 3 on both sides

(x-1)^2+ (y+1)^2=3 is the standard form

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