Expert: Ahmed Salami - 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 Jujuwarriah,
The general equation of a circle with center (a,b) and radius r is
(x-a)² + (y-b)² = r²
For the circle with center at (-5,-2) and passes through the origin, we know that the radius would be the distance from the center to any point on the circle and in this case one of such points is the origin.
The radius is therefore
r = √[(0--5)² + (0--2)²]
 = √[(0+5)² + (0+2)²]
 = √[5² + 2²]
 = √29
And so,
(x--5)² + (y--2)² = (√29)²
(x+5)² + (y+2)² = 29
x² + 10x + 25 + y² + 4y + 4 =29
x² + y² + 10x + 4y = 0
By the way, the circle x² + y² = 1 is the circle with center at the origin and having a radius of 1 unit.

Regards