Question

find the standard form of the equation for the circle with the following properties. center (2, -3/2) and tangent to the y - axis

Explanation:

Step1: Recall circle - standard - form formula

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Identify the center coordinates

Given the center of the circle is $(h,k)=(2,-\frac{3}{2})$.

Step3: Determine the radius

Since the circle is tangent to the $y$ - axis, the distance from the center of the circle to the $y$ - axis is the radius. The $x$ - coordinate of the center is 2, so the radius $r = 2$.

Step4: Substitute values into the formula

Substitute $h = 2$, $k=-\frac{3}{2}$, and $r = 2$ into the standard - form equation:
$(x - 2)^2+(y+\frac{3}{2})^2=2^2$.

Answer:

$(x - 2)^2+(y+\frac{3}{2})^2 = 4$