Question

write the equation in standard form for a circle with center (-6,7) and tangent to the x - axis.
the standard form of the equation of the circle is
(type an equation. simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

The standard - form 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

Given the center of the circle is $(h,k)=(-6,7)$.

Step3: Determine the radius

Since the circle is tangent to the $x$ - axis, the distance from the center of the circle to the $x$ - axis is the radius. The $y$ - coordinate of the center is $7$, and the distance from the point $(-6,7)$ to the $x$ - axis is $7$. So, $r = 7$.

Step4: Substitute values into the formula

Substitute $h=-6$, $k = 7$, and $r = 7$ into the standard - form equation: $(x+6)^2+(y - 7)^2=49$.

Answer:

$(x + 6)^2+(y - 7)^2=49$