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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q.254 (page 1156)

In the following exercises, write the standard form of the equation of the circle with the given information:
Radius is $9 u n i t s$ and center is $(- 3, 5)$

Short Answer

Expert verified

The equation of the circle is $x^{2} + y^{2} + 6 x - 10 y = 47$

Step by step solution

01

Given information

The radius of the circle is $9 u n i t s$ and center is at $(- 3, 5)$

02

use the standard form of equation and substitute the corresponding values

The standard form of equation can be given as ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

Substituting the values we get

role="math" localid="1645418504655" $(x - {(- 3))}^{2} + {(y - 5)}^{2} = 9^{2} {(x + 3)}^{2} + {(y - 5)}^{2} = 9^{2}$

Substituting the values we get,

role="math" localid="1645418536175" $x^{2} + 6 x + 9 + y^{2} - 10 y + 25 = 81 x^{2} + 6 x + y^{2} - 10 y = 47$

03

Conclusion

The equation of the circle is $x^{2} + 6 x + y^{2} - 10 y = 47$

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