2.2 Parallel and Perpendicular Lines and Circles Slopes and Parallel Lines 1. If two nonvertical lines are parallel, then they have the same slopes. 2. If two distinct nonvertical lines have the same slope, then they are parallel. 3. Two distinct vertical lines, with undefined slopes, are parallel.

Example 1: Writing Equation of a Line Parallel to a Given Line

Solution Y 1 =-7 X 1 =-2

What is the slope of the line? Given equation Slope of the line is –5.

X 1 =-2, y 1 =-7, and m=-5

Practice Exercise

Answer to the Practice Exercise

Slopes and Perpendicular Lines 1. If two nonvertical lines are perpendicular, then the product of their slopes is –1. 2. If the product of the slopes of two lines is –1, then lines are perpendicular. 3. A horizontal line having zero slope is perpendicular to a vertical line having undefined slope.

Example 2: Finding the Slope of a Line Perpendicular to a

Solution Solve the given equation for y. Slope is –3/2.

Given line has slope –3/2.

Practice Exercise

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Definition of a Circle A circle is the set of all points in a plane that are equidistant from a fixed point called the center. The fixed distance from the circle’s center to any point on the circle is called the radius.

The Standard Form of the Equation of a Circle Center Any point on the circle

Example 3 Finding the Standard Form of a Circle’s Equation

Solution

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Example 4: Using the Standard Form of a Circle’s

Solution

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The General Form of the Equation of a Circle

Example 5: Converting the General Form of Circle’s

Solution

h=-4 k=-2 r=2

Practice Exercise

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