Given a circle with center at $(3, 4)$ and radius $5$, find the equation of the circle.
Answer 1
Olivia Lee
The general equation of a circle with center at $(h, k)$ and radius $r$ is:
$(x – h)^2 + (y – k)^2 = r^2$
Here, $h = 3$, $k = 4$, and $r = 5$. Substitute these values into the equation:
$(x – 3)^2 + (y – 4)^2 = 5^2$
Simplifying further:
$(x – 3)^2 + (y – 4)^2 = 25$
Therefore, the equation of the circle is:
$(x – 3)^2 + (y – 4)^2 = 25$
Answer 2
Thomas Walker
To find the equation of a circle, we use the formula:
$(x – h)^2 + (y – k)^2 = r^2$
Here the center $(h, k)$ is $(3, 4)$ and the radius $r$ is $5$.
Substitute $h = 3$, $k = 4$, and $r = 5$ into the formula:
$(x – 3)^2 + (y – 4)^2 = 5^2$
Calculate $5^2$:
$(x – 3)^2 + (y – 4)^2 = 25$
The equation of the circle is:
$(x – 3)^2 + (y – 4)^2 = 25$
Answer 3
Chloe Evans
The equation of a circle is $(x – h)^2 + (y – k)^2 = r^2$.
Given center $(3, 4)$ and radius $5$:
$(x – 3)^2 + (y – 4)^2 = 25$
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