Expert: Paul Klarreich - 10/12/2009

Question
Hey, I'm in first year calculus in university and it seems my prof expects us to know the xy formula of a circle. I know all about functions with x and y values but never circles.

one sample question would be:

Find an equation of the circle that has center (-5, -2) and passes through the origin.
(x -   )2 + (y -   )2 =


Can you please tell me how I would do this and what the components of this circle formula mean? How do you arrange this formula to translate and transform this function? I think the primary fuctions is x^2 + y^2 =1.


Thanks so much.

Answer
Questioner: Gordon
Country: Canada
Category: Advanced Math
Private: No
Subject: circle formulae
Question: Hey, I'm in first year calculus in university and it seems my prof expects us to know the xy formula of a circle. I know all about functions with x and y values but never circles.

one sample question would be:

Find an equation of the circle that has center (-5, -2) and passes through the origin.
(x -   )2 + (y -   )2 =


Can you please tell me how I would do this and what the components of this circle formula mean? How do you arrange this formula to translate and transform this function? I think the primary fuctions is x^2 + y^2 =1.


Thanks so much
.........................................
If a circle has its center at  (h,k) and its radius is r, then its equation is:

(x - h)^2 + (y - k)^2 = r^2

For your example

Find an equation of the circle that has center (-5, -2) and passes through the origin.
(x -   )2 + (y -   )2 =

If the center is  (-5,-2), then you write:

(x -(-5))2 + (y - (-2))2 = r^2
(x + 5))2 + (y + 2)2 = r^2

But you don't have r. yet.  Use the distance formula to find the distance between (-5,-2) and (0,0).  That number is your r.