Sullivan Algebra and Trigonometry: Section 2.4

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Sullivan Algebra and Trigonometry Section 2.4

• Objectives
• Define Parallel and Perpendicular Lines
• Find Equations of Parallel Lines
• Find Equations of Perpendicular Lines
• Write the Standard Form of the Equation of a
  Circle
• Graph a Circle
• Find the Center and Radius of a Circle and Graph
  It

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Definitions Parallel Lines
Two lines are said to be parallel if they do not
have any points in common.
Two distinct non-vertical lines are parallel if
and only if they have the same slope and have
different y-intercepts.
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Find the equation of the line parallel to
y -3x 5 passing through (1,5).
Since parallel lines have the same slope, the
slope of the parallel line is m -3.
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Definitions Perpendicular Lines
Two lines are said to be perpendicular if they
intersect at a right angle.
Two non-vertical lines are perpendicular if and
only if the product of their slopes is -1.
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Example Find the equation of the line
perpendicular to y -3x 5 passing through
(1,5).
Slope of perpendicular line
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Definition A circle is a set of points in the
xy-plane that are a fixed distance r from a fixed
point (h, k). The fixed distance r is called the
radius, and the fixed point (h, k) is called the
center of the circle.
y
(x, y)
r
(h, k)
x
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Definition The standard form of an equation of a
circle with radius r and center (h, k) is
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Graph
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Step 1 Plot the center of the circle.
Step 2 Plot points above, below, left, and right
of the center by traveling a distance equal to
the radius.
Step 3 Graph the circle.
y
(-1, 7)
(3,3)
(-5, 3)
(-1,3)
x
(-1, -1)
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The general form of the equation of a circle is
To find the center, radius, and graph of a circle
in general form, first rewrite the equation of
the circle in standard form using the process of
completing the square.
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Find the center and radius of
Center (2,-4) Radius 5