Chapter 11: Q. 11.15 (page 1078)

ⓐ Find the center and radius, then ⓑ graph the circle: ${(x - 3)}^{2} + {(y + 4)}^{2} = 4$

Short Answer

Expert verified

The center and the radius of the circle are $(3, - 4)$ and $2$ respectively. The graph of this circle is:

Step by step solution

Step 1. Given information.

The equation of the circle is ${(x - 3)}^{2} + {(y + 4)}^{2} = 4$ .

We have to find radius and center.

Also, we have to graph this circle.

Part (a) Step 2. Compare with the standard form of a circle to find radius and center

Write the given equation ${(x - 3)}^{2} + {(y + 4)}^{2} = 4$ in standard form ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

${(x - 3)}^{2} + {(y + 4)}^{2} = 4 {(x - 3)}^{2} + {(y - (- 4))}^{2} = 2^{2}$

Therefore,

Centerrole="math" localid="1645258175838" $= (3, - 4)$

Radius $= 2$

Part (b) Step 3. Graph the circle using radius and center

The circle is graphed as:

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ⓐ Find the center and radius, then ⓑ graph the circle: ${(x - 3)}^{2} + {(y + 4)}^{2} = 4$

Short Answer

Step by step solution

Step 1. Given information.

Part (a) Step 2. Compare with the standard form of a circle to find radius and center

Part (b) Step 3. Graph the circle using radius and center

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ⓐ Find the center and radius, then ⓑ graph the circle:(x-3)2+(y+4)2=4

Short Answer

Step by step solution

Step 1. Given information.

Part (a) Step 2. Compare with the standard form of a circle to find radius and center

Part (b) Step 3. Graph the circle using radius and center

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

ⓐ Find the center and radius, then ⓑ graph the circle: ${(x - 3)}^{2} + {(y + 4)}^{2} = 4$