Chapter 11: Q.262 (page 1156)

In the following exercises, a) find the center and radius, then b) graph each circle:
$x^{2} + y^{2} - 6 x - 12 y - 19 = 0$

Short Answer

Expert verified

The center of the circle is at $(3, 6)$ and radius is $8$

The graph of the circle can be given as

Step by step solution

Given information

We are given a equation of the circle

$x^{2} + y^{2} - 6 x - 12 y - 19 = 0$

Separate the same variable and write then in quadratic equation form

We get,

$x^{2} - 6 x + y^{2} - 12 y - 19 = 0 x^{2} - 6 x + 9 - 9 + y^{2} - 12 y + 36 - 36 - 19 = 0 {(x - 3)}^{2} + {(y - 6)}^{2} - 64 = 0 {(x - 3)}^{2} + {(y - 6)}^{2} = 8^{2}$

Comparing with the standard equation

On comparing we get

The radius is $8 u n i t s$ and the center is at $(3, 6)$

Plot the graph of the equation

The graph of the equation can be given as

Conclusion

The center is at $(3, 6)$ and the radius is $8$

The graph of the circle can be given as

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In the following exercises, a) find the center and radius, then b) graph each circle:
$x^{2} + y^{2} - 6 x - 12 y - 19 = 0$

Short Answer

Step by step solution

Given information

Separate the same variable and write then in quadratic equation form

Comparing with the standard equation

Plot the graph of the equation

Conclusion

One App. One Place for Learning.

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Study anywhere. Anytime. Across all devices.

In the following exercises, a) find the center and radius, then b) graph each circle:x2+y2-6x-12y-19=0

Short Answer

Step by step solution

Given information

Separate the same variable and write then in quadratic equation form

Comparing with the standard equation

Plot the graph of the equation

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Discrete Mathematics

Decision Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, a) find the center and radius, then b) graph each circle:
$x^{2} + y^{2} - 6 x - 12 y - 19 = 0$