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Math Help - Orthoganal Projectories

  1. #1
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    Orthoganal Projectories

    Hello, I've recently encountered this problem: Prove these two equations are Orthoganal. x^2 + y^2 = r^2 | ax + by = 0 |

    I get stuck after I differentiate both sides.

    The left equation I get

    2x + 2yy'= 0

    = y' = -x/y

    And the then the rightside

    A + By' = 0

    = y' = -a/b

    I know I need to get rid of the A & B, but at the moment it's not clear to me. Any idea's on where to start? Thank you.
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  2. #2
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    Quote Originally Posted by Impalord View Post
    Hello, I've recently encountered this problem: Prove these two equations are Orthoganal. x^2 + y^2 = r^2 | ax + by = 0 |

    I get stuck after I differentiate both sides.

    The left equation I get

    2x + 2yy'= 0

    = y' = -x/y

    And the then the rightside

    A + By' = 0

    = y' = -a/b

    I know I need to get rid of the A & B, but at the moment it's not clear to me. Any idea's on where to start? Thank you.
    Divide the equation ax + by = 0 by bx to see that a/b = y/x.
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  3. #3
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    Also note that x^2+ y^2= r^2 is the equation of a circle with center at the origin while Ax+ By= 0 is the equation of a straight line through the origin. In other words, for all A, B, and r, the line is a diameter of the circle.
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