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Write the equation of the line, in slope-intercept form, that passes through (2, 4) and is perpendicular to

Warm-Up: October 13, 2015

Homework Questions?

Distance and Midpoint Formulas;

CirclesSection 1.3

The distance, d, between the points (x1, y1) and (x2, y2) is

Derived from the Pythagorean Theorem

The Distance Formula

212

212 yyxxd

The diameter of a circle has endpoints at (-5, 6) and (1, -1).

a) What is the diameter of the circle?b) What is the radius of the circle?

You-Try #1

The midpoint of a line segment with the endpoints (x1, y1) and (x2, y2) is

Average the x’s and average the y’s

The Midpoint Formula

2,

22121 yyxx

The diameter of a circle has endpoints (-1, -2) and (5, 4).

Where is the center of the circle?

You-Try #2

A circle is the set of all points in a plane that are equidistant from a fixed point, called the center.

The center is at (h, k) The fixed distance from the circle’s center

to any point on the circle is called the radius.

The radius is r.

Circle

Center at (h,k) Radius = r

The Standard Form of the Equation of a Circle

222 rkyhx

Write the standard form of the equation of the circle with center (-2, 1) and radius 6.

You-Try #4 (like HW #31-40)

1. Identify and graph the center.2. Identify the radius, r.3. Count out from the center r units in each

direction (up, down, right, left) and plot a point.

4. Draw a circle through those 4 points.

Graphing a Circle

State the center and radius of the circle described by the equation below and graph it

Example 5 (like HW #41-48)

932 22 yx

State the center and radius of the circle described by the equation below and graph it

You-Try #5 (like HW #41-48)

1613 22 yx

The General Form of the Equation of a Circle

022 FEyDxyx

Completing the Square Given , we can create a perfect square

trinomial by dividing by 2, squaring it, and adding it

Can complete the square for ’s and ’s separately.

Remember that whatever you add to one side, you must add to the other side

222

22

DxDDxx

Complete the square and write the equation in standard form. Then state the center and radius of the circle.

Example 6 (like HW #49-56)

0461222 yxyx

Complete the square and write the equation in standard form. Then state the center and radius of the circle.

You-Try #6 (like HW #49-56)

0912422 yxyx

Read Section 1.3 Page 148 #1-57 Odd

Give exact answers, not rounded decimals.

Assignment

In #1-18, find the distance between each pair of points. Give exact answers.

1) (2, 3) and (14, 8)3) (4, 1) and (6, 3)5) (0, 0) and (-3, 4)7) (-2, -6) and (3, -4)9) (0, -3) and (4, 1)11) (3.5, 8.2) and (-0.5, 6.2)

56,

31 and

51,

37)17

54,3 and 5,33)15

0,5 and 3,0)13

In Exercises 31-40, write the standard form of the equation of the circle with the given center and radius.

31) Center (0, 0), r=7 33) Center (3, 2), r=5 35) Center (-1, 4), r=2 37) Center (-3, 1), r= 39) Center (-4, 0), r=10 In Exercises 41-48, give the center and

radius of the circle described by the equation and graph each equation.

3

423)45

3613)43

16)41

22

22

22

yx

yx

yx