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The locus of the centre of the circle for which one end of the diameter is (3,3) while the other end lies on the line x+y=4.

The locus of the centre of the circle for which one end of the diameter is (3,3) while the other end lies on the line x+y=4.

Grade:12

1 Answers

Rup Chitrak
16 Points
9 years ago

let (h,k) be the centre of the circle and other end of diameter be (x1,y1).

h= (x1+3)/2      and        k= (y1+3)/2

or, x1=2h-3       and        y1=2k-3

but (x1,y1) lie on x+y=4,

(2h-3)+(2k-3)=4

or, h+k=5

for locus, replace (h,k) by (x,y)..

thus, locus is  x+y=5

 

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