# 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)...

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

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### 1 Answer

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.

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