Analytic Geometry ( F Elect 3 )

TAKE HOME QUIZ (  to be submitted on January 25,  2012 )

1.  Find the equation of the circle whose ends points of the diameter is on the point

     ( 3, 6 ) and  ( – 5 , – 4 ).

2.   a) Find the equation of the circle with radius of  6 units, having its center in the       

     second quadrant and tangent to the axes. b) Solve the same problem if the center

     of the circle is on the third quadrant.

3.  Find the equation of the circle with center at ( –3 , – 4 ) and passing through the  

      origin.

4.  Fine the equation of the circle tangent to the line 4x – 3y + 20 = 0  and having              

     its center  at  ( 5, 5).

5. Determine the center and radius of the following circles and draw the graph:

      a)    x² + y² +  6x – 10y  = 15

      b)    x²  +  y²  – 10x + 8y – 23 = 0

      c)    x²  +  y²  + 10x – 8y – 8  = 0

6. Find the equation of the circle tangent to the x-axis at ( 5, 0) with a radius of  4

     units  and with center ( a ) in the fourth quadrant and  ( b ) in the first quadrant.

7.  Express the following statement into an equation :  the point    is at a                                      

     distance 4 from the point ( 3, 90°).

8.  Sketch the graph of the polar equation    .