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About Azeem Hussain
Expertise
I can answer virtually any kind of question dealing with of Math 536 and below, my forte being in parabolic functions and analytical geometry. I'm currently learning Linear Algebra, and cannot answer questions that deal with subject matter more advanced than that.

Experience
I am neither a professor nor a teacher of this subject. I am merely a student who is gifted at mathematics and enjoys being of service to his community. I frequently tutor people in math and the results are usually great.

Publications
Reflections, Riverside School Board (2005, 2006)

Education/Credentials
Diploma of Secondary Studies from Chambly Academy High School, and IBO-MYP certificate as well. My lowest mark on a high school math final was 97%, peaking at 99% in 2006 and 2007 (second-highest Math 436 mark in the province). Being a Quebecer, I am fluent in English and French and can respond to questions easily in both languages.

Awards and Honors
Pascal Math Competition, School Champion(2007)

You are here: Experts > Science > Math for Kids > Geometry > Circle Formulae

Geometry - Circle Formulae

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

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