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Chapter 2: Problem 39

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-4,0), r=10$$

Short Answer

Expert verified
The standard form of the equation of the circle with the given center and radius is \[ (x + 4)^2 + y^2 = 100 \]

Step by step solution

01

Identify given parameters

The given center of the circle is (-4,0) and the radius is 10. Hence, in our formula h=-4, k=0, and r=10.
02

Substitute into the formula

Substitute the identified parameters into the standard form of the circle: \[ (x - (-4))^2 + (y - 0)^2 = (10)^2 \]
03

Simplify the equation

Simplify the equation to obtain the standard form by simplifying the brackets and squaring the radius: \[ (x + 4)^2 + y^2 = 100 \]

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