What is the equation of the circle with a center at $(4 ,1 )$ and a radius of $5$ ?

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Answer 1 · 2018-03-28T01:00:23

See a solution process below:

The equation for a circle is:

$(x - color(red)(a))^2 + (y - color(red)(b))^2 = color(blue)(r)^2$

Where $(color(red)(a), color(red)(b))$ is the center of the circle and $color(blue)(r)$ is the radius of the circle.

Substituting the values from the problem gives:

$(x - color(red)(4))^2 + (y - color(red)(1))^2 = color(blue)(5)^2$

$(x - color(red)(4))^2 + (y - color(red)(1))^2 = 25$

graph{((x - 4)^2 + (y - 1)^2 - 0.06)((x - 4)^2 + (y - 1)^2 - 25) = 0 [-15, 15, -7.5, 7.5]}

What is the equation of the circle with a center at (4 ,1 )(4 ,1 ) and a radius of 5 5 ?