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Math Help - [SOLVED] write an equation for a circle

  1. #1
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    [SOLVED] write an equation for a circle

    write an equation of a circle whos center is at (3,-1) and tangent to the line y=4

    what i got so far is this

    (x-3)^2 + (y+1)^2 = r^2

    what is throwing me off is this tangent of y=4
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by john doe View Post
    write an equation of a circle whos center is at (3,-1) and tangent to the line y=4

    what i got so far is this

    (x-3)^2 + (y+1)^2 = r^2

    what is throwing me off is this tangent of y=4
    The tangent is giving you a hint on the value of the radius.

    Since the center is at (3,-1), the tangent line y=4 is the equation of the line that limits how far the point on a circle can be from its center.

    So the distance from (3,-1) to (3,4) is what?

    It shouldn't be much of a hassle now to get the answer you're looking for.

    I hope this helps!

    --Chris
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  3. #3
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    I see now but why'd they have to add tangent of y=4 was that just to confuse me?
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  4. #4
    Moo
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    Quote Originally Posted by john doe View Post
    I see now but why'd they have to add tangent of y=4 was that just to confuse me?
    No, it means that the distance from the center to the tangent equals the radius

    See this:


    OM is the distance from the center to the tangent.

    What Chris used is the fact that the tangent y=4 is horizontal. Thus the line OM is vertical, that is to say any point on this have the same abscissa. Furthermore, M is on the tangent, so its ordinate y is 4.
    This is why he asked you to compute the distance from (3, -1) to (3, 4)
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