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About Paul Klarreich
Expertise
I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience
I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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You are here: Experts > Science > Mathematics > Advanced Math > Equation of a circle

Advanced Math - Equation of a circle

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.

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