Finding Center & Radius of Circle C

[thomas49th]

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 :)

 

[Tedjn]

Once you do one of these, you'll know how to do them all. Try completing the square for both variables.

 

[thomas49th]

(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

 

[Tedjn]

You have a x² and a y². How would you get it into the form (x-a)² and (y-b)²?

 

[thomas49th]

sorry I am not sure :( did i complete the square correctly?

 

[Defennder]

It's sort of only a bit correct. The equation of a circle is $(x-x_0)^2 + (y-y_0)^2 = r^2$, where $x_0$ and $y_0$ 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.

 

[thomas49th]

Thanks! :)