Question

Please help meee!!!!

A circle has its center at (1, 4) and a radius of 2 units. What is the equation of the circle?

(x − 1)2 + (y − 4)2 = 4

(x + 2)2 + (y + 4)2 = 2

(x + 1)2 + (y − 4)2 = 4

(x − 1)2 + (y − 4)2 = 2

Answer 1

The equation of a circle is just (x-h)^2+(y-k)^2= r^2
in place of h you just put the x-coordinate of the center
in place of k you put the y-coordinate of the center
and in place of r you put the radius
So your answer is just (x-1)^2+(y-4)^2=4 (first choice)

Answer 2

A.
`(x-1)^2+(y-4)^2=4`

Explanation:

We have been given that a circle has its center at (1, 4) and a radius of 2 units. We are asked to write the equation of the given circle.

Since we know that the center-radius form of circle equation is:

`(x-h)^2+(y-k)^2=r^2`, where (h,k) is the center of circle and r is radius of circle.

Upon substituting our given values in above format we will get,

`(x-1)^2+(y-4)^2=2^2`

`(x-1)^2+(y-4)^2=4`

Therefore, the equation of our given circle is
`(x-1)^2+(y-4)^2=4` and option A is the correct choice.