Question

I need help with this question please, my exam is tomorrow.

Answer 1

Center: (2,2)

Radius: 2

Answer 2

Answers:

Center = (2,2)

Radius = 2

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Step-by-step explanation:

Consider (A+B)^2 = A^2+2AB+B^2 after using the FOIL rule.

If A = x, then we have (x+B)^2 = x^2+2Bx+B^2

The coefficient of the x term is 2B. It divides in half to get B, and it squares to B^2 as the final term.

In short, if we want to complete the square on something like x^2-4x, then we do two things:

• Divide the x coefficient in half
• Square the result

So we go from -4 to -2 after dividing in half, and then from -2 to 4 after squaring. We'll add 4 to both sides to complete the square for the x terms.

`x^2+y^2-4x-4y+4 = 0\\\\(x^2-4x)+(y^2-4y)+4 = 0\\\\(x^2-4x+4)+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y)+4 = 4\\\\`

We'll do the same thing for the y terms. Though notice we already have a +4 on the left side. So we can have it absorb into the y terms parenthesis grouping like so

`(x-2)^2+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y+4) = 4\\\\(x-2)^2+(y-2)^2 = 4\\\\`

Now compare that to the circle template

`(x-h)^2 + (y-k)^2 = r^2`

We see that

• h = 2
• k = 2
• r = 2

This circle has its center at (h,k) = (2,2)

The radius is r = 2