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The sum of the squares of the length of ...

The sum of the squares of the length of the chords intercepted on the circle `x^(2)+y^(2)=16`, by the lines x +y = n , `n in N`, where N is the set of all natural numbers, is

A

160

B

320

C

105

D

210

Text Solution

Verified by Experts

The correct Answer is:
D
`x+y=n` will be intersecting
`x^2+y^2=16" if " n = 1,2,3,4,5("n " inN)`
Length `OL=n/(sqrt(2))` (Distance of from origin)
OM=4 (radius)
`MN=2sqrt(16-n^2/2)`
`(MN)^2=4(16-n^2/2)`
`sum_(n=1)^(5)4(16-n^2/2)=4[16xx5-(5xx6xx11)/(2xx6)]=320-110=210`
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