Expert: Alon Mandes - 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
Hello Gordo,
Yes , the circle equation in x-y plane is : x^2+y^2=r^2. Where r is the radius. But, this
equation describes a circle that is centered in the origin (0,0) .
The equation for a circle that is centered in any point (a,b) in the x-y plane is :
(x-a)^2+(y-b)^2=r^2 .
In the given exercise above , we may certainly write :
(x--5)^2+(y--2)^2=r^2
(x+5)^2+(y+2)^2=r^2.
All we have to find now is the radius r. In order to do so, we use the given information :
"This circle passes through the origin". That means : the distance between the point (-5,-2)
%26 the origin is the length of the radius ..
To find distance between 2 points (a,b) %26 (c,d) we use the formula :
d=√[(a-c)^2+(b-d)^2] . therefore,
r=√[(-5-0)^2+(-2-0)^2]=√[25+4]=√29 .
%26 now the equation will become :
(x+5)^2+(y+2)^2=29.

Alon.