Question

write the standard form of the equation of the circle with its center at (-6,0), and a radius of 5. 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 the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Substitute the given values into the formula

Given \(h=-6\), \(k = 0\), and \(r = 5\). Substitute these into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-6))^2+(y - 0)^2=5^2\).

Step3: Simplify the equation

Simplify \((x + 6)^2+y^2=25\).

Answer:

\((x + 6)^2+y^2=25\)