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Chapter 6

Test Yourself

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01:23

Put the equation of each c…

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(a) find the center $(h, k…

01:44

Find the center and the ra…

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Find the center and radius…

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cancer. We have let H Kama K b the centre and they're radius of the circle. True's equation as X squared plus two experts y squared minus four y plus one is equal to zero. What is the value of H plus? Que was r So we know that our standard equation for a circle this X minus h squared, Let's fly minus case squared is equal to R squared. So we need to get this equation right here to model this one a little bit more closely. So we know that the first thing that we want to do is to move the one over to the other side, at which point we're gonna have X squared was too X. What's Y squared? Minus four Y is equal to negative one from here. We want to complete the square, complete the square, so we're going to need to break it up into the ex components and the Y components. So for completing the square here, well, we need to do is take the B value, divide that by two, square it and add that to both sides. So the value here is to the to divide by two. Is one one square to stole one. So we're going to be adding one to both sides. So now we've got X squared plus two x plus one plus y squared minus four Y is equal to zero. We're gonna go ahead and do the same thing for the why the negative for over two squared is going to be four positive force. We're going toe at Fort. Both sides get X squared plus two x plus one. That's why squared minus four y plus four is equal to four. So then, from here now, these two components right here, our factory ble. So we're going to go ahead and factor that and get X plus one squared. Plus why minus two squared is equal to four. From here, we know our H Kama K is our center point. So we know our center point is negative. One common, too. And our radius is going to be the square root of whatever values on the right side. So that should be two of her. Adding negative one plus two plus two that should give us three to A C is air correct Answer

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