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![[Post New]](/templates/default/images/icon_minipost_new.gif) 22 Mar 2007 23:12:32 IST
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A circle with centre (2,-1) have a tangent 3x+y=0.Find the equation of the other tangent which passes through the origion?? explain ur answer
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22 Mar 2007 23:35:12 IST
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You cannot control circumstances.....
But you can control thinking over them...... |
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22 Mar 2007 23:43:54 IST
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first find the radius of the circle using the centre co-ordinates and the equation of the tangent which is given......... Then using the radius and the centre find out the equation of the circle..... Then by using this... ( in circle equation) x.x1 + y.y1 + g( x + x1) + f( y+y1) + c = 0 put (x1, y1) as (0.0) as the tangent passes through origin.... is this right? sorry can't post the complete solution..
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You cannot control circumstances.....
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22 Mar 2007 23:54:45 IST
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seriously ,But i feel there is some problem in my solution itself .....can neone point it out... i think it related to he tangency condition..?????
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You cannot control circumstances.....
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23 Mar 2007 00:01:41 IST
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A circle with centre (2,-1) have a tangent 3x+y=0.Find the equation of the other tangent which passes through the origion??
assume the circle in the general form
then center is given, substitute values of -g ,-f
then xx1 + yy1 + 2gx + 2fy +c = 0 , represents a tangent at (x1,y1)
but 3x + y =0
compare coefficients.
proceed to get the circles eqn
then find thr reqd, tangent !
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23 Mar 2007 00:47:05 IST
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23 Mar 2007 01:25:45 IST
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A circle with centre (2,-1) have a tangent 3x+y=0.Find the equation of the other tangent which passes through the origion??
radius(R)= perp dist from center to tangent...
R = | (6-1)/ 10 | = 5/10 =  (5/2) ==>R2 = 5/2
eqn of circle (x-2)2 + (y+1)2 = 5/2 ..............1
any tangent from origin y = mx
putting in 1
(x-2)2 + (mx+1)2 = 5/2
x2 + 4 - 4x + (mx)2 + 1 + 2mx = 5/2
=> (1+m2) x2 - (4 - 2m) x + 5 = 5/2
=> (1+m2) x2 - (4 - 2m) x + 5/2 = 0
since it is tangent, therefore delta = 0
(4 - 2m)2 - 10(1+m2) = 0
=> 3m2 + 8m -3 = 0
m = -3 and 1/3
so eqns are y = -3x and y = x/3
or y + 3x = 0 and 3y - x = 0 ......ans
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Truly Mittal
B.Tech IIT Guwahati
trulymittal@gmail.com |
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23 Mar 2007 01:29:44 IST
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to prevent confusion i want to tell something about radius from sharma sir, r=mod[5/  10] =mod[ 5/ 2] hence ,r2=5/2 P.S:i was stranded here for some time as was missing in 2.so i thought of clearing it thank you sirs bye,
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