Finding Center & Radius of Circle C

In summary, the circle C has a centre at the point (5,0) and a radius of √7. The equation of the circle is (x-5)² + y² = 7. To find the coordinates of the centre and the radius, complete the square for both variables and substitute the resulting expressions back into the equation of the circle.
  • #1
thomas49th
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0

Homework Statement

The circle C, with the centre at the point A, has equation x² + y² - 10x + 9 = 0

Find:

a) the co-ordinates of A,

b) the radius of C

Homework Equations



(x-a)² + (y-b)² = r²

The Attempt at a Solution



... not sure what to do really. any suggestions

thanks :)
 
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  • #2
Once you do one of these, you'll know how to do them all. Try completing the square for both variables.
 
  • #3
(x²-5) -16
(y²)+9=0

so does this mean (5,0) is the co-ordinate.
is the radius sqrt(16-9) = sqrt(7)

?

thanks
 
  • #4
You have a x2 and a y2. How would you get it into the form (x-a)2 and (y-b)2?
 
  • #5
sorry I am not sure :( did i complete the square correctly?
 
  • #6
It's sort of only a bit correct. The equation of a circle is [itex](x-x_0)^2 + (y-y_0)^2 = r^2[/itex], where [itex]x_0[/itex] and [itex]y_0[/itex] are the coordinates of the centre and r is the radius.

Complete the square for x^2 - 10x + 9 first, then substitute the resulting expression back into the question, and move the constant to the RHS. You'll get the equation of circle.
 
  • #7
Thanks! :)
 

1. What is the formula for finding the center of a circle?

The formula for finding the center of a circle is (h, k), where h is the x-coordinate and k is the y-coordinate of the center point. This can also be represented as (x - h)^2 + (y - k)^2 = r^2, where r is the radius of the circle.

2. How do you find the radius of a circle if you know the center point?

To find the radius of a circle if you know the center point, you can use the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) is the center point and (x2, y2) is any other point on the circle. This distance will be equal to the radius of the circle.

3. Can the center of a circle be located outside of the circle?

No, the center of a circle must always be located within the circle. If the center is located outside of the circle, it is not a true circle.

4. How many points are needed to determine the center of a circle?

You need at least three points to determine the center of a circle. These points can be any three points on the circumference of the circle, and can be used to create a triangle. The center of the circle will be the intersection of the perpendicular bisectors of this triangle.

5. Can you find the center and radius of a circle if you only know the equation of the circle?

Yes, you can find the center and radius of a circle if you only know the equation. By rearranging the equation into standard form (x - h)^2 + (y - k)^2 = r^2, you can determine the center point (h, k) and the radius r.

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