I'm having trouble understanding the concept of this maths question x^2+y^2......?

Question

x^2 + y^2-2x+4y-4=0


and I'm supposed to find the center and radius of each circle

this qustion is about a circle?

should I add/subtract the like terms

what would x^2-2x be then and so on???????????? **********

Answer 1

ok so first group the x's
x^2-2x+y^2+4y-4=0
now we complete the square
x^2-2x+1+y^2+4y+4=4-1-4
(x-1)^2+(y+2)^2=-1


see if that helps

Answer 2

Tackle this problem algebraically: simplify by grouping like terms, then look for factors that make sense. Here's a step by step solution:

Step 1: Group like terms - separate x and y factors.

x^2 - 2x + 0 + y^2 + 4y - 4 = 0.

Step 2: Rewrite the equation without the constant factor. (We will put numbers in these blanks later that will add up to -4).

x^2 - 2x + __ + y^2 + 4y + __ = 0.

Step 3: Factor the x terms and y terms (separately). You are lucky, because the factors of these polynomials are easy to spot:

x^2 - 2x +1 factors to (x-1)^2.

y^2 + 4y - 5 factors to (y + 5) (y -1)

Step 4: Notice that the two constants we used, 1 and -5, add up to -4. So, we can substitute these factors back into the original equation:

(x - 1)^2 + (y+5)(y+1) = 0

Step 5: Solve by asking, at what points is this equation true?

Clearly, x =1 causes the x factor to be 0.
y = -5 causes the y factor to be 0.
So does y = 1.

So, I think the answer is that the two points (1, -5) and (1, 1) satisfy the original equation.

Let's check that answer by substituting back into the original equation.
for x=1 and y= - 5:
(1) ^2 + (-5)^2 - 2(1) + 4 (-5) - 4 = 0.
1 + 25 - 2 - 20 - 4 = 0
26 - 26 = 0. True!
So (1, -5) solves the equation.

for x =1 and y = 1:
(1)^2 + (1)^2 - 2 (1) + 4(1) - 4 = 0
1 + 1 - 2 + 4 - 4 = 0.
2 - 2 + 4 - 4 = 0. True!
So, (1, 1) solves the equation.

So, the answer to this math question is that this equation is true at two points: (1, -5) and (1, 1).

Answer 3

(x² - 2x) + (y² + 4y) = 4
(x² - 2x + 1) + (y² + 4y + 4) = 4 + 5
(x - 1)² + (y + 2)² = 9
(x - 1)² + (y - (-2))² = 3²
Centre (1 , - 2)
Radius = 3