# Thread: coordinate geometry of circles

1. ## 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

2. [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

I will try to help.
Center of first circle 3,2

Plot and id the two tangents.No cals required

Center of second circle 2,2
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

3. Hello, wale!

Did you make any sketches?

$1.\;\;(x-3)^2 +(y-2)^2\:=\:36$

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?

$2.\;\;(x-2)^2 +(y-2)^2 \:=\:32$

Find the coordinates of the endpoints of the diameter whose equation is $y=x$
Code:
              |
| * * *
* |         *   *
*   |           o
*    |         *  *
|       *
*     |     *       *
*     |   o (2,2)   *
*     | *           *
- - - - + - - - - - - - - - -
*  * |            *
o   |           *
*   * |         *
| * * *
|

We want the intersections of: . $\begin{Bmatrix}[1] & (x-2)^2 + (y-2)^2 \:=\:32 \\ [2] & x\:=\:y \end{Bmatrix}$

Substitute [2] into [1]: . $(x-2)^2 + (x-2)^2 \:=\:32 \quad\Rightarrow\quad 2(x-2)^2 \:=\:32$

. . . . . . . $(x-2)^2 \:=\:16 \quad\Rightarrow\quad x-2 \:=\:\pm4 \quad\Rightarrow\quad x \:=\:2 \pm 4$

Hence: . $x \;=\;6,\:-2 \quad\Rightarrow\quad y \;=\;6,\:-2$

Therefore, the endpoints of the diameter are: . $(6,6)\,\text{ and }\,(\text{-}2,\text{-}2)$