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Callisto
Group Title
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
 one year ago
Callisto Group Title
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
 one year ago

This Question is Closed

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

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

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

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

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

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

Callisto Group TitleBest ResponseYou've already chosen the best response.2
Algebra matters.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.2
C = (0, 2)
 one year ago

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

Callisto Group TitleBest 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)
 one year ago

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

Callisto Group TitleBest ResponseYou've already chosen the best response.2
I 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.
 one year ago

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

Callisto Group TitleBest ResponseYou've already chosen the best response.2
A = (6, 0)
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.2
D = (4, 0)
 one year ago

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

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

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

Callisto Group TitleBest ResponseYou've already chosen the best response.2
equation 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)
 one year ago

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

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

hartnn Group TitleBest ResponseYou've already chosen the best response.2
no, u are correct.
 one year ago

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

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

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

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.1
where 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)
 one year ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.2
as we know slope of OC
 one year ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.1
yep..exactly..
 one year ago

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

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

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

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

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

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

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

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