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Callisto
 2 years 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
Callisto
 2 years 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

This Question is Closed

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

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

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

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

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

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

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

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

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

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

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

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

hartnn
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.2Not so relevant. dw:1356789503661:dw

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

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

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

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

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

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