Question

write the standard form of the equation of the circle with its center at $(-7,0)$, and a radius of 7. what is the equation of the circle in standard form? (simplify your answer.)

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Identify the values of \(h\), \(k\), and \(r\)

Given the center \((-7,0)\), so \(h=-7\), \(k = 0\), and radius \(r = 7\).

Step3: Substitute the values into the standard - form equation

Substitute \(h=-7\), \(k = 0\), and \(r = 7\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x-(-7))^2+(y - 0)^2=7^2\).

Step4: Simplify the equation

\((x + 7)^2+y^2=49\)

Answer:

\((x + 7)^2+y^2=49\)