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1 Find the Centre and Radius of the circle x? +y2 + &x-4y+4=0...

Question

1 Find the Centre and Radius of the circle x? +y2 + &x-4y+4=0

1 Find the Centre and Radius of the circle x? +y2 + &x-4y+4=0



Answers

Find the center and radius for each circle.
$$x^{2}+y^{2}=1$$

Okay, So completing the square on the X is I'm gonna have, uh, x squared. No bother. X minus 1/2 square. And for the why I'm gonna have live plus 1/2 squared. In both cases, I had to add 1/4 to to both to complete the square seven a have 1/2 on the right, Simon of 1/2 plus 1/4 plus 1/4 1 which is just equal to one. Therefore, my center is just gonna be at 1/2 negative one. And my radius will just be equal to the square root of one, which is one. Okay, thank you.

Okay, we're given this equation finance center and the radius of the circle. So first step let's that's at 1/4 to both sides of the equation. OK I have x squared minus two. X plus one plus y squared minus y plus 1/4 equals 1/4. Okay, next step, okay let's complete the square. Mhm. So I have X -1 squared plus. Why might this one half squared? Because 1/4? Yeah. Okay. This is a completing the square and according to this equation or this formula or whatever you call this, Okay. We can identify that the center of the circle. Okay, center of the circle if was and what half? And the really is is 1/2? Okay. Yeah. Yeah.

We need to find the center of the circle and the radius of the circle. Our equation for circle follows X. The form x minus h squared plus y minus k squared is equal to our square, so r h matches up, but this had to be rewritten with a minus or x minus a negative one, so H is negative one, K is positive one and r squared is 16. Our center comes from hk We got a chess being negative one and K is being positive one. So our center is negative one positive one. R radius comes from our, so we have r squared is equal to 16, so we're gonna take the square root of both sides and we get our is equal to four. So our center is located at negative one positive one and our radius is four.

So this problem we're looking for the center and the radius of this circle were given the form of the equation that looks like this. Okay, so the first thing that I'm going to do is I'm going to organize my variables. So I have X squared minus x leave a little space. Why squared? Plus, why leave a little space, subtract 14 to put that on the other side. Okay, so let's complete the square in this case, cutting one negative one in half becomes cutting 1.5 comes one half squaring become 1/4 adding 1/4 to both sides. And then this will leave me with X minus one half squared. Okay. Taking positive one. Cutting it in half will give me one half and squaring. That will give me 1/4. Somebody had 1/4 negative. 14 That positive 1/4 will cancel, leaving me with a positive 1/4 on the right hand side of the equation. This will leave me with y. Plus one half squared is equal toe. One half, 1/4. So in this case, the center which is always the opposite of what's in the place will be positive, one half negative one half. And the radius, which will be square root cause a squared plus B squared equals C squared will equal one half. So we're gonna start here and go one half in each direction.


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