Question

What is the general equation of a circle centered at the point (h, k)?

Answer 1

Not sure how to explain this without giving the answer o.o
(x-h)^2 + (y-k)^2 = r^2
Its basically the pythagorean theorem, a^2 + b^2 = c^2, just in a different form.

Answer 2

you should just give me the answer lol

Answer 3

x2+y2=1

Answer 4

thats the answer

Answer 5

is that the answer

Answer 6

well a circle centered at \((h,k)\) is defined to be the set of all points \(r\) away from the center; recall that we can compute distance using the Pythagorean theorem as @Psymon pointed out:$$\sqrt{(x-h)^2+(y-k)^2}=r$$Squaring both sides yields the familiar 'circle equation' in Cartesian coordinates:$$(x-h)^2+(y-k)^2=r^2$$

Answer 7

so would it be x2+y2=1

Answer 8

that is the equation for the unit circle centered at the origin, not a general circle centered at a point \((h,k)\)

Answer 9

so what is the answer

Answer 10

if \(f(x,y) = x^{2} + y^{2} \) for a circle, centered at the origin, then a circle, centered at (h,k), would be \(f(x-h,y-k)\). Note that radius is \( \sqrt{f(x,y)} \). Plug and play. @oldrin.bataku summarized it for you explicitly.