Question

write the standard form of the equation of the circle with its center at (-1,0), and a radius of 10. 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 \((-1,0)\), so \(h=-1\), \(k = 0\), and radius \(r = 10\).

Step3: Substitute the values into the standard form

Substitute \(h=-1\), \(k = 0\), and \(r = 10\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x-(-1))^2+(y - 0)^2=10^2\).

Step4: Simplify the equation

Simplify \((x + 1)^2+y^2=100\).

Answer:

\((x + 1)^2+y^2=100\)