Question

A circle has its center at (−1, 2) and a radius of 3 units. What is the equation of the circle?

Answer 1

(x+1) ^2 + (y-2)^2 = 9
This is the answer and this is how you get it (below)
(x – h)^2 + (y – k)^2 = r^2

Answer 2

Answer: The required equation of the circle is
`x^2+y^2+2x-4y=4.`

Step-by-step explanation: We are given to find the equation of a circle with center at the point (-1, 2) and a radius of 3 units.

We know that

the standard equation of a circle with center at the point (h, k) and radius of length r units is given by

`(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

For the given circle, we have

center , (h, k) = (-1, 2) and radius, r = 3 units.

Therefore, from equation (i), we get

`(x-(-1))^2+(y-2)^2=3^2\\\\\Rightarrow (x+1)^2+(y-2)^2=9\\\\\Rightarrow x^2+2x+1+y^2-4y+4=9\\\\\Rightarrow x^2+y^2+2x-4y=4.`

Thus, the required equation of the circle is
`x^2+y^2+2x-4y=4.`