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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. 43 (page 1083)

In the following exercises, 鈸� identify the center and radius, and 鈸� graph.
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

Short Answer

Expert verified

(a) Center of the circle $x^{2} + y^{2} - 4 x + 10 y - 7 = 0$ is $(2, - 5)$ and radius is $6$

(b) graph of the circle is

Step by step solution

01

Step 1. given data

The given equation of the circle is

$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

02

Step 2. Part (a)

Group the x-terms and y-terms

$x^{2} + y^{2} - 4 x + 10 y - 7 = 0 (x^{2} - 4 x) + (y^{2} + 10 y) = 7$

complete the squares

$(x^{2} - 4 x + 4) + (y^{2} + 10 y + 25) = 7 + 4 + 25 {(x - 2)}^{2} + {(y + 5)}^{2} = 36$

Compare the equation with the standard equation of the circle

${(x - 2)}^{2} + {(y - (- 5))}^{2} = 6^{2} {(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

so center $(h, k) = (2, - 5)$

radius $r = 6$

03

Step 3. Part (b)

Plot the circle of center $(2, - 5)$ and radius $6$

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