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`        A point moves such that the sum of the squares of its distance from the sides of a square of side unity is equal to 9. Show that the locus is a circle whose centre coincides with the centre of the square. Find also its radius`
7 years ago

419 Points
```										Dear Debadutta
Let us take a simple square having four vertices at (.5,.5),(-.5,.5),(.5,-.5),(-.5,-.5),
Point is (x1,y1)
So according to question
(x1+.5)^2+(y1+.5)^2+(x1+.5)^2+(y1-.5)^2+(x1-.5)^2+(y1+.5)^2+(x1-.5)^2+(y1-.5)^2=9
4x12+4y12=9-8*.52=7
So we can see  locus is a circle whose centre coincides with the centre of the square and radius of circle is square root of 7/4.
All the best.
AKASH GOYAL

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7 years ago
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