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Math Help - Graph transformations - circle

  1. #1
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    Graph transformations - circle

    Hello!

    I am unsure about how to determine if the origin is located inside, outside or on the circle or ellipse after a graph transformation. For example, given the equation of the circle to be (x+3)^2 + (y-4)^2 = 5 , how do I know if the origin is within or outside or a point on the graph itself? How about in the case of an ellipse?

    Thank you!
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  2. #2
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    Hello, Tangera!

    I am unsure about how to determine if the origin is located inside,
    outside or on the circle or ellipse after a graph transformation.

    For example, given the equation of a circle: (x+3)^2 + (y-4)^2 \:= \:5^2
    how do I know if the origin is within or outside or a point on the graph itself?
    How about in the case of an ellipse?
    A little thought will give you the answer . . .

    What does it mean when a point in on a graph?
    . . It means that the coordinates of the point satisfy the equation.


    Given the circle: (x+3)^2 + (y-4)^2\:=\:5^2

    Where is the origin (0,0) relative to the circle?
    . . Substitute x=0,\:y=0\!:\;\;(0+3)^2 + (0-4)^2 \;=\;3^2 + (-4)^2 \;\;{\bf{\color{blue}= \;25}}
    (0,0) satisfies the equation . . . The origin is on the circle.

    Where is (1,3) ?
    . . Substitute x=1,y=3\!:\;\;(1+3)^2 + (3-4)^2 \:=\:16 + 1 \:=\:17 \;\;{\bf{\color{blue}<\:25}}
    (1,3) is inside the circle.

    Where is (3,5) ?
    . . Substitute x=3, y=5\!:\;\;(3+3)^2 + (5-4)^2 \:=\:37\;\;{\bf{\color{blue}> \;25}}
    (3,5) is outisde the circle.


    The same procedure applies to ellipses.

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  3. #3
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    I get it! I get it!! Thank you very very much!!
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