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Thread: cartesian inequality

  1. #1
    Junior Member
    Mar 2008

    cartesian inequality

    Find the Cartesian inequation for the region represented by

    Please put your answer in a "natural" form
    What is the centre of that circle for real numbers x, y
    What is the radius of the circle

    The locus of points satisfied by the relation is

    If any one knows where there are good online math resources to do with cartesian inequations can you let me know
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  2. #2
    Super Member

    May 2006
    Lexington, MA (USA)
    Hello, samdmansam!

    Find the Cartesian inequality for the region represented by:
    $\displaystyle |z+9-9i| \;\leq \; \frac{1}{7}|z-3-2i|$

    Write your answer in a "natural" form.
    What is the centre of that circle?
    What is the radius of the circle?
    We have: .$\displaystyle \bigg|z-(-9+9i)\bigg| \;\leq\; \frac{1}{7}\bigg|z - (3+2i)\bigg| $

    We are given two points on the complex plane: .$\displaystyle A(-9,9)\:\text{ and }\:B(3,2)$

    We want all points $\displaystyle P(x,y)$ such that: .$\displaystyle d(PA) \:\leq \:\frac{1}{7}\,d(PB)$

    . . $\displaystyle d(PA) \;=\;\sqrt{(x+9)^2 + (y-9)^2}\qquad d(PB) \;=\;\sqrt{(x-3)^2 + (y-2)^2}$

    We have: .$\displaystyle \sqrt{(x+9)^2 + (y-9)^2} \;\leq \;\frac{1}{7}\sqrt{(x-3)^2 + (y-2)^2} $

    . . which simplifies to: .$\displaystyle 48x^2 + 888x + 48y^2 - 878y + 7925 \;\leq \;0$

    Now complete the square to find the center and radius of this circle.
    . .
    We want all points on and inside the circle.

    Good luck!

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