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SHATABDI MUKHERJEE

FIND THE EQUATIONS OF THE CIRCLES WHICH PASS THROUGH THE ORIGIN AND CUT OFF EQUAL CHORDS OF^{[ ]}

2 UNITS FROM THE LINES Y=X AND Y= -X.

rashmi varma

hi...this is a very basic ques...let me do it from a basic method

gaurav chaudhary

since the circle passes through origin c=0
eqn of circle x^2 +y^2 2gx+ 2fy=0
length of chord =(2)^1/2
prep . dis. from origin to line y=x => |-g+f|/(2)^1/2
from line y = -x => |g+f|/(2)^1/2

(radius)^2 = (prep. dis)^2 + { [(2)^1/2]/2 }^2
using this we get two eqn.
(g+f)^2 = 1
(g-f)^2 = 1
solve to get values g &f
4 circles are possible

rashmi varma

let the eqn of circle be (x-a)^2+(y-b)^2=r^2

as circle passes thru origin

a^2+b^2=r^2

the two lines intersect at origin and circle passes thru it

join centre of circle(a,b) to origin.

draw perpendiculars from the centre to the chords.both segments are of length 1/root 2. chords make angle 45 degree with radius.apply pyth. u get radius.

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