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Math Help - Cat and mouse

  1. #1
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    Question Cat and mouse

    Okay so .....

    A mouse is running a donut-shaped track with equation:

    (X-4)^2 + (Y-3)^2 = 4

    At the same time a cat is running a coplanar intersecting opaque track with equation:

    [(X-4)^2] 9 + [(Y-3)^2] 1 = 1

    What are the four possible coordinates of the intersections (simultaneous solutions) where the mouse might catch the cat?


    Thanks so much if you can help me out
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  2. #2
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    Quote Originally Posted by gdunne18 View Post
    ]A mouse is running a donut-shaped track with equation:
    (X-4)^2 + (Y-3)^2 = 4
    At the same time a cat is running a coplanar intersecting opaque track with equation:
    (X-4)^2/ 9 + (Y-3)^2/ 1 = 1
    What are the four possible coordinates of the intersections (simultaneous solutions) where the mouse might catch the cat?...
    Hello,

    there are a lot of different ways to get the 4 points. In this case it would be the best to do the calculations like this:

    (X-4)^2 + (Y-3)^2 = 4 ===> (Y-3)^2 = 4 - (X-4)^2

    (X-4)^2/ 9 + (Y-3)^2/ 1 = 1 ===> (Y-3)^2 = 1 - (X-4)^2/ 9 Therefore:

    4 - (X-4)^2 = 1 - (X-4)^2/ 9 ===> 3 = (X-4)^2 - (X-4)^2/ 9

    3 = (8/9)*(X-4)^2 ===> (27/8) = (X-4)^2 (******)

    x = 4 (3/4)*√(6)

    Use this (*****) result to calculate y:

    (Y-3)^2 = 4 - (X-4)^2 ===> (Y-3)^2 = 4 - (27/8) = (5/8)

    y = 3 (1/4)*√(10)

    The 4 points are:
    (4 + (3/4)*√(6), 3 + (1/4)*√(10)); (4 + (3/4)*√(6), 3 - (1/4)*√(10)); (4 - (3/4)*√(6), 3 - (1/4)*√(10)); (4 - (3/4)*√(6), 3 - (1/4)*√(10))

    EB
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  3. #3
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    Hello, gdunne18!

    A mouse is running a circular track with equation: .(x - 4) + (y - 3) .= .4

    At the same time a cat runs a track with equation: .(x - 4)/9 + (y - 3) .= .1

    What are the four possible coordinates of the intersections
    where the mouse might catch the cat?

    We have: . (x - 4) + .(y - 3) . = .4 . [1]
    . . . .and: . (x - 4) + 9(y - 3) -= .9 . [2]

    Subtract [1] from [2]: .8(y - 3) .= .5
    . . . . . . . . . . . . . . . . .__
    Solve for y: .y .= .3 √10/4
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ._
    Substitute into [1] and solve for x: .x .= .4 3√6/4

    . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . __
    The intersections are: . (4 3√6/4, 3 √10/4)

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  4. #4
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    thanks so much you guys big help thanks again
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