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Chapter 2: Problem 36

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-3,5), r=3$$

Short Answer

Expert verified
The equation of the circle in standard form is \((x+3)^2 + (y-5)^2 = 9\).

Step by step solution

01

Identify the center and radius

Given that the center of the circle, represented as \((a, b)\), is \((-3, 5)\), a is -3 and b is 5. The radius is given as 3.
02

Input in the circle's equation

Now use the values of a, b, and r to fill in the standard formula of the circle's equation \((x-a)^2 + (y-b)^2 = r^2\). This gives us \((x-(-3))^2 + (y-5)^2 = 3^2\).
03

Simplify the equation

By simplifying the equation, we get: \((x+3)^2 + (y-5)^2 = 9\). This is the equation of the circle in standard form.

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Most popular questions from this chapter

The regular price of a pair of jeans is \(x\) dollars. Let \(f(x)=x-5\) and \(g(x)=0.6 x\) a. Describe what functions \(f\) and \(g\) model in terms of the price of the jeans. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the jeans. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the jeans, \(f \circ g\) or \(g \circ f ?\) Explain.

Does \((x-3)^{2}+(y-5)^{2}=0\) represent the equation of a circle? If not, describe the graph of this equation.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25\) and \((x-2)^{2}+(y+3)^{2}=36\)

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$f(x)=4-x, g(x)=2 x^{2}+x+5$$

Give an example of a circle鈥檚 equation in standard form. Describe how to find the center and radius for this circle.
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