Question

write the equation in standard form of a circle with center (-2,7), tangent to the y - axis. the standard form of the equation for the circle is (type an equation. simplify your answer.)

Explanation:

Step1: Recall the standard - form of a circle equation

The standard - form of a circle equation 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 of the circle

The center of the circle is given as $(-2,7)$, so $h=-2$ and $k = 7$.

Step3: Determine the radius of the circle

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 $-2$, and the distance from the point $(-2,7)$ to the $y$ - axis is $| - 2|=2$. So $r = 2$.

Step4: Substitute the values of $h$, $k$, and $r$ into the standard - form equation

Substitute $h=-2$, $k = 7$, and $r = 2$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x+2)^2+(y - 7)^2=4$.

Answer:

$(x + 2)^2+(y - 7)^2=4$