Expert: Azeem Hussain - 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
Hi Chundarpatpotato,

The equation for the unit circle centred at the origin is x²+y²=1.  The standard equation is (x-h)²+(y-k)²=r² for a circle of radius r centred at the point (h,k).

Solving such equations isn't really any different than any other equation, but it can get a bit messy.  Whenever you take a square root, it is imperative that you take the positive and the negative root.

Now, for the sample question.  Plug in the values of h and k.
(x-h)²+(y-k)²=r²
(x-(-5))²+(y-(-2))²=r²
(x+5)²+(y+2)²=r²

The origin is at (0,0), so plug those in for x and y.  Now isolate r².
(0+5)²+(0+2)²=r²
25+4=r²
29=r²

(It is of interest to note that you just applied the Pythagorean Theorem.)  Thus, the equation of the circle in question is (x+5)²+(y+2)²=29.

Thanks for asking,
Azeem