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 one year ago
Haven't done circle for long :(
In the figure, a circle S: \(x^2+y^2+6x2y=0\) 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 xaxis at D.
Find the coordinates of B
 one year ago
Haven't done circle for long :( In the figure, a circle S: \(x^2+y^2+6x2y=0\) 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 xaxis at D. Find the coordinates of B

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Callisto
 one year ago
Best ResponseYou've already chosen the best response.2dw:1356781451262:dw

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1solve these equations for \( x_1, y_1 \), \[ x_1^2 + y_1^2 + 6x_1−2y_1=0,\\ x_2^2 + y_2^2 + 6x_2  2y_1 = 0, x_2=0, y_2 \neq 0 \\ (x_1x_2)^2 + (y_1y_2)^2 = 20\]

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2May I know what (x2, y2) is??

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1x_2, y_2 are the coordinates of C

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1probably you would end up with two sets of point, choose the the point where y>0

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1sorry ... this equation .. change y1 to y2 \[ x_2^2 + y_2^2 + 6x_2  2y_1 = 0, x_2=0, y_2 \neq 0 \\ \]

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1yes!! sorry i was careless ... did you find out answer?

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2\(x^2 + y^2 +6x  2y =0\) (1) \(x^2+(y2)^2 =20\) => \(x^2 + y^2 4y+4 =20\) (2)

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2Do you mean I knew the answer?

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2I knew the answer, yes. I'm looking for a way to get the answer. I tried once (more than once) but I thought I was making it too complicated. I just wanted to find a simpler way so that my sister can do it easily.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2coordinates of A can also be found similarly.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2then u know equation of line BD can't u use that to find coordinates of B ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2solving equation of line and circle simultaneously.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2are u sure about D =(4,0)??

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2equation of line BD: \[\frac{y2}{x} = \frac{2}{4}\]\[x = 42y\] \[(42y)^2 + y^2 +6(42y)  2y =0\] \[5y^2  30y + 40=0\]\[y=4, 2\]When y=4, x = 42(4) = 4 When y=2, x=42(2) =0 (rejected) So, B= (4, 4) Yay! Much simpler :) Thanks!!! @hartnn Yes! Yes! D = (4,0)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2oh, i somehow got 36 instead of 40, thats why i was stuck.....

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2Correction: o.O Did I make a mistake? :S

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2Okay, thanks again! I didn't thought of the line. I'm just too stupid :(

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2happens! i just did a silly mistake of 6*4 =20 :P

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.1did anyone notice : dw:1356789155290:dw

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.1where thats the center we know coordinates of C let center be O hence we know slope of OB slope given, distance give, we can find coordinate! B)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2how do we know slope of OB?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2given slope of OB and O, we can find B, no need of any distance..

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2Not so relevant. dw:1356789503661:dw

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.1ohh yes!! COA are collinear !

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2how does that make it any simpler ?

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.1i dont know,,just a good fact to know! :D

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2''Not so relevant.'' :P

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2u got 2 more easy methods ;)

Callisto
 one year ago
Best ResponseYou've already chosen the best response.2Yes! Yes! Thanks! Thanks!!
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