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![[Post New]](/templates/default/images/icon_minipost_new.gif) 3 Jun 2007 20:37:56 IST
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A circle of radius 2 has center at (2,0). A circle of radius 1 has center at (5,0). A line is tangent to the two circles at points in the first quadrant. Which of the following is the y-intercept of the line?
a) 3
b) 2/4
c)8/3
d) 2 2
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3 Jun 2007 20:41:21 IST
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hi
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3 Jun 2007 20:43:11 IST
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bye
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3 Jun 2007 20:45:24 IST
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Experts pls. help!!!!!!
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3 Jun 2007 20:45:28 IST
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i think its a wrong Q coz the slope of the line is coming out 2 be imaginary,,the line cant touch the 2 circles simultaneously
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3 Jun 2007 20:49:55 IST
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r u sure the Q is right?
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3 Jun 2007 20:54:49 IST
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The question is 100% correct!!!
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3 Jun 2007 20:55:45 IST
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Draw the figure.
The circles meet at one point only (4,0).
At this point the tangent is parallel to Y axis.
Hence y intercept is infinity
The options seem incorrect.
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3 Jun 2007 20:59:46 IST
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ellesar ur absolutely right but hey,,the Q is still wrong, it says the line is tangent to the circle at a point in the first quadrant but the point is 4,0 i.e on the x-axis plzz people make sure the Qs are correct bfre postin'em
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3 Jun 2007 23:12:53 IST
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either the question is wrong or the options are wrong...
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PLEASE RATE MY ANSWERS IF YOU FIND THEM USEFUL... |
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3 Jun 2007 23:15:18 IST
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Let me tell you socciboy that the question was obtained from the Bansal sample test papers which is very rarely incorrect.
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look hope u got the figure rite cuz i obviously cant draw it here...
its basically 2 externally touching circles wid a direct common tangent in 1st quadrant...
now join centre of circle wid radius 2 to the point of contact of tangent to this same circle....let the angle made by this line wid x axis b @...then the point of contact of tangent 2 the two circles r respectively...(2 cos @, 2 sin @) and (cos @, sin @)...thus slope of tangent = tan@....
now also observe tht the tangent itself makes an angle..(90 + @) wid positive x-axis...thus its slope being (- cot @)..
thus...- cot@ = tan @ or @ = 135 degrees...
also (2 cos@, 2 sin@) lies on dis line..
so eqn of line is y= - x + 4/(2^0.5)..
hence y intercept wud b 2 * (2^0.5)...i.e, option d
hope u got it...
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4 Jun 2007 08:15:37 IST
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Thanks a lot naveen.
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6 Jun 2007 05:09:45 IST
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Sorry for the wrong solution. Didn't see the first quadrant.
Excellent solution naveen
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