Analytic Geometry Review

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Analytic Geometry Review

• MA151 Calculus

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Some things you should remember
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(No Transcript)
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Distance Formula

• The distance between the points P1(x1, y1) and
  P2(x2, y2) is

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Remember

• The distance between points a and b on a number
  line is a - bb - a .
• Also, dont forget about the Pythagorean Theorem.
  
• Both are used when deriving the Distance Formula.

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y
P2(x2, y2)
y2
P1(x1, y1)
P3(x2, y1)
y1
x
x1
x2
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Equation of a Circle

• An equation of the circle with center (h, k) and
  radius r is
• (x - h)2 (y - k)2 r2
• In particular, if the center is the origin (0,
  0), the equation is
• x2 y2 r2

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y
P(x,y)
r
k
C(h,k)
x
h
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Slope

• The slope if a nonvertical line that passes
  through the points P1(x1, y1) and P2(x2, y2) is
• The slope of a vertical line is not defined.

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Point-Slope Form of the Equation of a Line

• An equation of the line passing through the point
  P1(x1, y1) and having slope m is
• y y1 m(x x1)

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Slope-Intercept Form of the Equation of a Line

• An equation of the line with slope m and
  y-intercept b is
• y mx b

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Parallel and Perpendicular Lines

• Two nonvertical lines are parallel if and only if
  they have the same slope.
• Two lines with slopes m1 and m2 are perpendicular
  if and only if m1m2 -1 that is, their slopes
  are opposite reciprocals