Circle Geometry

thomas49th

1. The problem statement, all variables and given/known data


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

2. Relevant equations

(x-a)² + (y-b)² = r²


3. 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 im not sure :( did i complete the square correctly?

Defennder

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.

thomas49th

Thanks!!! :)