Thread: coordinate geometry of circles

1. (x-3)^2 +(y-2)^2=36
find equations of the two horizontal tangents to the circle

2.(x-2)^2 +(y-2)^2 =32
Find coordinates of the endpoints of the diameter whose equation is y=x

please respond quickly

[quote=wale;487298]1. (x-3)^2 +(y-2)^2=36
find equations of the two horizontal tangents to the circle

2.(x-2)^2 +(y-2)^2 =32
Find coordinates of the endpoints of the diameter whose equation is y=x

please respond quickly[/quote

Need answers fast?
I will try to help.
Center of first circle 3,2
radius of circle is 6

Plot and id the two tangents.No cals required


Center of second circle 2,2
radius of circle is 4radical 2
Plot the center point and draw in y=x start at origin line has slope = 1 extend line above and below the x axis
draw in two slope diagrams using the center as reference point but the rise and the run must be 4 so that the hypothenus will be 4 rad 2. No cals required


bjh

Hello, wale!

Did you make any sketches?

Find the equations of the two horizontal tangents to the circle.

Code:

              | 
              | (3,8) 
        - - - + * o * - - -
            * |   :     *
          *   |   :       * 
         *    |   : r=6    * 
              |   : 
        *     |   :         *
        *     |   o(3,2)    *
        *     |   :         * 
              |   : 
      ---*----+---:--------*-----
          *   |   :       *
            * |   :     *
        - - - + * o *  - - - 
              | (3,-4) 
              |

Got it?

Find the coordinates of the endpoints of the diameter whose equation is

Code:

              |
              | * * * 
            * |         *   *
          *   |           o
         *    |         *  *
              |       *
        *     |     *       * 
        *     |   o (2,2)   *
        *     | *           *
      - - - - + - - - - - - - - - -
         *  * |            *
          o   |           *
        *   * |         *
              | * * *
              |

We want the intersections of: .


Substitute [2] into [1]: .

. . . . . . .

Hence: .


Therefore, the endpoints of the diameter are: .