find center and radius of the circle given by the equation?

Question

x square + y squere -4x+2y=4

Answer 1

I'll rewrite the question for you, because we usually denote ^ as "to the power of" for simplicity.

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

We have to do a process called completing the square, for both the x and y variables. So first, let's group all the x terms together and y terms together.

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

To complete the square, we have to add 4 to the x terms and 1 to the y terms. Since we're adding 4 and 1 to the left hand side, we have to do the same to the right hand side.

x^2 - 4x + 4 + y^2 + 2y + 1 = 4 + 4 + 1

Now, we factor those now square polynomials.
(x-2)^2 + (y+1)^2 = 9

The center of the circle is given by the values in the brackets, but the negative of them. In the above case, the center is at (2,-1), since you take the negative of -2 (the value next to the x) and 1 (the value next to the y).

To get the radius, you take the square root of the right hand side, so the square root of 9 is 3.

Answer 2

the customary equation for a circle based at (h, ok) with radius r is: (x - h)² + (y - ok)² = r² subsequently, our circle relies at (-4, 9), so h = -4, and ok = 9. Its radius is 12, so r = 12. And, our customary equation turns into: (x - (-4))² + (y - 9)² = 12² => (x + 4)² + (y - 9)² = a hundred and forty four

Answer 3

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

the general equation ofa circle is x^2 + y^2 + 2gx +2fy+c = 0
where(-g,-f)is the center of circle
and sqrt (g^2+f^2-c) is radius

hence center of this circle is (2,-1)
and radius is sqrt (4+1+4)=sqrt 9=3

Answer 4

You need to complete the square for x and complete the square for y.

You do know what I mean, don't you?

Add and subtract a constant that allows you to absorb x^2, and x terms into something like:

(x-k)^2...

Do the same for y, then all the extra constants can be combined to give the radius squared on the right hand side.

Answer 5

That's an intriguing geometry problem. What is YOUR question? What work have you done so far? Where have you looked to find information about doing this? Where did you get stuck? Be specific, please.

Answer 6

Try your textbook or this site;

http://www.valdosta.edu/~alazari/math1111/Circle