Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 − 4x + y2 + 8y = −4

Answer 1

I dont understand because the circle equation is (x-h)^2+(y-k)^2=r^2 and there are pluses instead of minuses and a negative radius but if it's been squared already how does that work?????

Answer 2

@mrm @RhondaSommer @Mehek14

Answer 3

@doc.brown can you help?

Answer 4

Beats me, man. If the radius were a multiple of \(i\) you could get a negative by squaring. Are you learning about imaginary numbers?

Answer 5

No I did a bit in algebra but this is my last thing in geometry and we haven't discussed them once.

Answer 6

Here's what you have: x2 − 4x + y2 + 8y = −4
Here's the standard formula: (x-h)^2+(y-k)^2=r^2

h and k are the x- and y- coordinates, respectively, of the center of the circle. r is the radius of the circle, and r^2 is the square of that radius.

You must manipulate your x2 − 4x + y2 + 8y = −4 algebraically (applying especially "completing the square". Have you used this before? If not, can you find a reference to "completing the square" in your textbook or online learning materials?

Your x2 − 4x + y2 + 8y = −4 must be re-written so that it has the form

x^2 - 4x + a - a + y^2 + 8y + b - b = -4.

Where does "a" come from? Take the coefficient of the x term (which is -4), halve it, and square the result. For example, if that coefficient were 12, you'd take half of that, which is 6, and square that result, obtaining 36.

OK: let's get to work:

x^2 - 4x + a - a + y^2 + 8y + b - b = -4.

What is the coefficient of x?
What is half of that?
What is the square of your result from above?
Replace "a" with the result of your work.

Then do the same thing for the "y" terms.

Answer 7

x^2 - 4x + a - a + y^2 + 8y + b - b = -4.

What is the coefficient of x?
What is half of that?
What is the square of your result from above?
Replace "a" with the result of your work.

Then do the same thing for the "y" terms.