Haven't done circle for long :(
In the figure, a circle S: $x^2+y^2+6x-2y=0$ cuts the axes at the origin O, A and C. A point B lies on the circle S so that the length of BC is $2 \sqrt{5}$ units. BC is produced to cut the x-axis at D.
Find the coordinates of B

Question

callisto · Answer

|dw:1356781451262:dw|

callisto · Answer

brb

experimentx · Answer

solve these equations for $ x_1, y_1 $, 
$$ x_1^2 + y_1^2 + 6x_1−2y_1=0,\
 x_2^2 + y_2^2 + 6x_2 - 2y_1 = 0, x_2=0, y_2 \neq 0 \
(x_1-x_2)^2 + (y_1-y_2)^2 = 20$$

callisto · Answer

May I know what (x2, y2) is??

experimentx · Answer

x_2, y_2 are the coordinates of C

experimentx · Answer

probably you would end up with two sets of point, choose the the point where y>0

experimentx · Answer

sorry ... this equation ..  change y1 to y2 
$$  x_2^2 + y_2^2 + 6x_2 - 2y_1 = 0, x_2=0, y_2 \neq 0 \ $$

callisto · Answer

Algebra matters.

callisto · Answer

C = (0, 2)

experimentx · Answer

yes!! sorry i was careless  ... did you find out answer?

callisto · Answer

$x^2 + y^2 +6x - 2y =0$  ---(1)
$x^2+(y-2)^2 =20$  =>  $x^2 + y^2 -4y+4 =20$  ---(2)

callisto · Answer

he?