Analytical Geometry | 27369 - according to an fiitjee study book-askIITians

anmol nanda Grade: 11

        according to an fiitjee study booklet of 2008-2010

concept:intercepts by circle on axis

we have formulas for intercept of circle

now it is given that

if circle tocuhes x-axis length of intercept on x-axis is 0.

But even when intercept length is 0 it dose not mean it should touch the axis it can be placed above the axis also?in  that case intercept is also 0?

8 years ago

Answers : (2)

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vikas askiitian expert

509 Points

							dear anmol , i m taking eg of ur previously asked q
x^2+y^2-8x+4y+4=0 ,         (let this is the eq of circle)
(g,f) =(-4,2) , C = 4

length of Y intercept = 2(f²-c)^1/2 
length of X intercept = 2(g²-c)^1/2 
if y intercept is 0 then f²=c               (condition 1 , touches y axis)

if x intercept is 0 then g²=c              (condition 2 , touches x axis)

from eq of circle ,  only condition 1 is satisfied so  this circle touches only y axis...
now its center is at (4,-2) so this circle is in fourth quadrant ,only 1 circle is possible for this 
condition....
position of circle is determined by its center ...
 now if u still have confusion then ask  on this forum...

8 years ago

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Durgesh Prasher

21 Points

this concept is truely true but converse is not true . u can say if a circle touches x axis then intercept is zero but for intercept =0 it may or maynot be true

8 years ago

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