The equation of a circle is given by x^2 - 4x + y^2 + 6y = 12 Select, inside, outside, or in to indicate where each coordinate pair is located in relation to the circle.

Question

(-1, -7)	choose
(-1, 3)	choose
(5, -7)	choose
(4, 1)	choose

Answer 1

Determine equation of circle by completing the square

x^2 - 4x + y^2 + 6y = 12

x^2 - 4x + 4 + y^2 + 6y + 9 = 25

(x-2)^2 + (y+3)^2 = 25

center is (2,-3) and radius is 5

Compute distance between each point and the center. If it equals 5, then it is on the circle. If it is greater then 5 it is outside the circle. If it is less than 5 it is inside the circle.

For example. (-1,-7). Distance from (2,-3) = sqrt( (2--1)^2 + (-3--7)^2) = sqrt (25) = 5 --> it is on the circle