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Identify the center and radius. From the equation, the graph is a circle centered at the origin with radius. r = 36 = 6. EXAMPLE 1. Graph an equation of a circle. Graph y 2 = – x 2 + 36 . Identify the radius of the circle . SOLUTION. STEP 1.

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slide1
Identify the center and radius. From the equation, the graph is a circle centered at the origin with radius

r= 36 = 6.

EXAMPLE 1

Graph an equation of a circle

Graphy2 = – x2 + 36. Identify the radius of the circle.

SOLUTION

STEP 1

Rewrite the equationy2 = – x2 + 36in standard form asx2 + y2 = 36.

STEP 2

slide2
EXAMPLE 1

Graph an equation of a circle

STEP 3

Draw the circle. First plot several convenient points that are 6 units from the origin, such as (0, 6), (6, 0), (0, –6), and (–6, 0). Then draw the circle that passes through the points.

slide3
The radius is

= 29

r = (2 – 0)2 + (–5 – 0)2

= 4 + 25

29

EXAMPLE 2

Write an equation of a circle

The point (2, –5) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.

SOLUTION

Because the point (2, –5) lies on the circle, the circle’s radius rmust be the distance between the center (0, 0) and (2, –5). Use the distance formula.

slide4
Use the standard form withr to write an equation of the circle.

=29

= (29 )2

Substitute for r

29

EXAMPLE 2

Write an equation of a circle

x2 + y2 = r2

Standard form

x2 + y2

x2 + y2 = 29

Simplify

slide5
A line tangent to a circle is perpendicular to the radius at the point of tangency. Because the radius to the point

(1–3, 2)has slope

=

=

2 – 0

2

– 3 – 0

3

EXAMPLE 3

Standardized Test Practice

SOLUTION

m

slide6
y –2= (x – (–3))

y –2= x +

y =

x+

13

2

ANSWER

3

3

3

3

9

2

2

2

2

2

The correct answer is C.

EXAMPLE 3

Standardized Test Practice

the slope of the tangent line at (–3, 2) is the negative reciprocal of or An equation of

2

3

the tangent line is as follows:

Point-slope form

Distributive property

Solve for y.

slide7
for Examples 1, 2, and 3

GUIDED PRACTICE

Graph the equation. Identify the radius of the circle.

1.

x2 + y2 = 9

3

SOLUTION

slide8
2.

y2 = –x2 + 49

for Examples 1, 2, and 3

GUIDED PRACTICE

SOLUTION

7

slide9
for Examples 1, 2, and 3

GUIDED PRACTICE

3.

x2 – 18 = –y2

SOLUTION

2

slide10
for Examples 1, 2, and 3

GUIDED PRACTICE

4. Write the standard form of the equation of the circle that passes through (5, –1) and whose center is the origin.

x2 + y2 = 26

SOLUTION

5. Write an equation of the line tangent to the circle x2 + y2=37 at (6, 1).

SOLUTION

y = –6x + 37

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