Chapter 11: Q. 41 (page 1083)

In the following exercises, ⓐ identify the center and radius, and ⓑ graph.
$x^{2} + y^{2} + 2 x + 6 y + 9 = 0$

Short Answer

Expert verified

(a) Center of the circle $x^{2} + y^{2} + 2 x + 6 y + 9 = 0$ is $(- 1, - 3)$ and radius is $1$

(b) graph of the circle is

Step by step solution

Step 1. given data

The given equation of the circle is

$x^{2} + y^{2} + 2 x + 6 y + 9 = 0$

Step 2. Part (a)

Group the x-terms and y-terms

$x^{2} + y^{2} + 2 x + 6 y + 9 = 0 (x^{2} + 2 x) + (y^{2} + 6 y) = - 9$

complete the squares

role="math" localid="1645116279245" $(x^{2} + 2 x + 1) + (y^{2} + 6 y + 9) = - 9 + 9 + 1 {(x + 1)}^{2} + {(y + 3)}^{2} = 1$

Compare the equation with the standard equation of the circle

${(x - (- 1))}^{2} + {(y - (- 3))}^{2} = 1^{2} {(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

so center $(h, k) = (- 1, - 3)$

radius $r = 1$

Step 3. Part (b)

Plot the circle of center $(- 1, - 3)$ and radius $1$

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In the following exercises, ⓐ identify the center and radius, and ⓑ graph.
$x^{2} + y^{2} + 2 x + 6 y + 9 = 0$

Short Answer

Step by step solution

Step 1. given data

Step 2. Part (a)

Step 3. Part (b)

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In the following exercises, ⓐ identify the center and radius, and ⓑ graph.x2+y2+2x+6y+9=0

Short Answer

Step by step solution

Step 1. given data

Step 2. Part (a)

Step 3. Part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

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Study anywhere. Anytime. Across all devices.

In the following exercises, ⓐ identify the center and radius, and ⓑ graph.
$x^{2} + y^{2} + 2 x + 6 y + 9 = 0$