Find an equation of the circle with center at (-2,3) that is tangent to the y-axis in the form of (x-a) ^2 + (y-b) ^2=c where a, b, c are constants.

hello:

the center is : (a, b) when : a = - 2 and b = 3

an equation y-axis is x = 0

the ridus is the distance betwen the center and y-axis:

r = | (1) (-2) + (0) (3) + 0 | / √ ((1) ² + (0) ²) = 2/1 = 2

so : c=4 ... (c = r²)

an equation of the circle is : (x+2) ² + (y-3) ² = 4