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Math Help - About vector intersection

  1. #1
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    Unhappy About vector intersection

    Where does the line <x,y>=<4t,3t> intersect the circle x^2+y^2=25?

    I am quite not sure about my solution and my answer.

    From <x,y>=<4t,3t>
    =>> x=4t and y=3t
    Then, substitute x and y to x^2+y^2=25.
    ==>> 16t^2+9t^2=25
    ==>> t^2=1
    ==>> t=+1,-1

    At t=1,-1 is the intersection point?
    And is this what the question asked?
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  2. #2
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    Quote Originally Posted by noppawit View Post
    Where does the line <x,y>=<4t,3t> intersect the circle x^2+y^2=25?

    I am quite not sure about my solution and my answer.

    From <x,y>=<4t,3t>
    =>> x=4t and y=3t
    Then, substitute x and y to x^2+y^2=25.
    ==>> 16t^2+9t^2=25
    ==>> t^2=1
    ==>> t=+1,-1

    At t=1,-1 is the intersection point?
    And is this what the question asked?
    Points given in Cartesian coordinates are probably required.

    t = 1 => (4, 3).

    t = -1 => (-4, -3).

    The answer is easily understood if you draw a graph of the circle and the line.
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