Question

consider the following nonlinear system of equations.

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step 1 of 3: determine the type and key parts of the graph of the first equation.
answer
selecting an option will display further inputs to complete your answer.
circle center: ( , ) radius:

Explanation:

Step 1: 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 of the circle and \(r\) is the radius.

Step 2: Identify the center and radius for the given equation \((x - 2)^2+(y + 1)^2 = 36\)

For the equation \((x - 2)^2+(y+1)^2 = 36\), we can rewrite \(y + 1\) as \(y-(-1)\).
Comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 2\), \(k=-1\), and \(r^2 = 36\).
Since \(r^2 = 36\), then \(r=\sqrt{36}=6\).

Answer:

center: \((2,-1)\) ; radius: \(6\)