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Parallel and Perpendicular Lines, Circles, and Graphing Techniques

Learn to define, find equations, and graph parallel and perpendicular lines along with writing and graphing circles in algebra and trigonometry. Practice identifying centers, radii, and equations of circles in standard and general form.

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Parallel and Perpendicular Lines, Circles, and Graphing Techniques

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  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. Example: Find the equation of the line perpendicular to y = -3x + 5 passing through (1,5). Slope of perpendicular line:

  6. 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

  7. Definition: The standard form of an equation of a circle with radius r and center (h, k) is

  8. 2 2 ( x + 1 ) + ( y - 3 ) = 16 Graph

  9. 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)

  10. 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.

  11. Find the center and radius of Center: (2,-4) Radius: 5

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