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vats mittal Grade: 12
        


the equation of the locus of the middle point of a chord of the circle x^2 + y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is:


 


(a)x+y=2


(b)x-y=2


(c)2x-y=1


(d)none of these


 


I WILL B VERY THANKFUL TO U IF U GIVE AN ELABORATED SOLUTION...THANKU


6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

let one of the line is y=mx                   (line is passing through origin)


this line makes an angle @ with x axis ...another line is also inclined to x axis with same angle but its slope will be -m..


now other will be y=-mx


let point of contact of line y=mx & y=-mx with circle be P & q respectively then


on solving y=mx and circle we get


P=[  2(1+m)/1+m2   ,   2m(1+m)/1+m2  ]


and on solving y=-mx and circle we get


q=[  2(1-m)/1+m2   ,   2m(m-1)/1+m2   ]


we have to find the locus of mid point of PQ because pq is chord of circle,


let X,Y is the mid point then


            X=2/1+m2  &  Y=2m2 /1+m2


on solving these we get


                X+Y=2


THIS IS THE REQUIRED EQUATION

6 years ago
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