The equation of a circle centered at the origin is x^2 + y^2 = 1.
The equation of a transformation 2 units to the left and 3 units up would be:
a) (x+2)^2 + (y-3)^2 = 1
b) (x-2)^2 + (y +3)^2 = 1
c) (x-3)^2 + (y+2)^2 = 1
d) (x+3)^2 + (y-2)^2 = 1
The equation of a circle with center at `(a, b)` with radius, `r` , is given by the following:
`(x - a)^2 + (y - b)^2 = r^2`
The given circle has the following equation:
`x^2 + y^2 = 1`
which means that it is centered at the origin, `(0, 0)` , and has radius, `r = sqrt(1) = 1.`
Now, we want to move it two units to the left and three units up. Moving to the left means translating to the negative direction of the x-axis. Starting from the origin, we end up at `(-2, 0)` . Moving up means moving towards the positive direction of the y-axis. Starting from the new point, we move three units up and end up at `(-2, 3)` . Now, `a = -2` and `b = 3`. Hence, the equation of our new (or translated circle) is:
`(x - (-2))^2 + (y - 3)^2 = 1`
`(x + 2)^2 + (y-3)^2 = 1`
Therefore, the answer is letter A.
Note: The radius didn't change.