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Math Help - Problems about coordinates(geometry)

  1. #1
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    Problems about coordinates(geometry)

    Please help me with these problems....^^;;

    Write an equation of the circle described.
    1. Center at the origin; radius 9.

    2. Center (-1,2); radius 5.

    3. Find the center and the radius of the circle (x+2)^+(y-3)^=36.

    Thank you ....
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  2. #2
    Moo
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    Hello,

    There is a direct way for it, by knowing the equation of a circle. Since I don't remember it, I'll show you how to retrieve it

    Any point on the circle will be at distance R from the center, where R is the radius.
    Let this point have coordinates (x,y) (yes, it will be the variables ).

    Sketch a circle (see the attached picture).
    Then let A be (x_0,y_0), that is to say coordinates of the center. Let B the point with coordinates (x,y).
    a and b will be two perpendicular lines, intersecting in D.

    What you want is that AB is always equal to R, the radius of the circle.

    Now, how are we going to get it ? Thanks to the Pythagorean theorem.

    The distance AD will be the difference between the absciss of A and B. This means that it will be AD=(x-x_0)

    The distance BD will be the difference between the ordinates of A and B. So it's BD=(y-y_0)

    Applying the theorem, we have :

    AB^2=BD^2+AD^2

    Hence \boxed{R^2=(x-x_0)^2+(y-y_0)^2}



    Take for example your first circle.
    R=9 and x_0=0 and y_0=0

    So just replace it in the equation
    Attached Thumbnails Attached Thumbnails Problems about coordinates(geometry)-circle.png  
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  3. #3
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    Quote Originally Posted by sarayork View Post
    Please help me with these problems....^^;;

    Write an equation of the circle described.
    1. Center at the origin; radius 9.

    2. Center (-1,2); radius 5.

    3. Find the center and the radius of the circle (x+2)^+(y-3)^=36.

    Thank you ....
    (1) was shown by Moo...

    You can do (2) similarly with x_0 = -1, y_0 = 2 and R = 5.

    For (3) compare Moo's formula for a circle, and obtain the values of x_0, y_0 and R
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