Find the sum of square of the length of the chords intercepted by the line x+y=n;n∈ N on the circle x2+y2=4 .

Question

Find the sum of square of the length of the chords intercepted by the line x+y=n;n∈ N on the circle x2+y2=4 . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-hn1jdoxkkaseosjr.jpg" /> AB=2AM AB2=4AM2 4(4 - (n2/2))=2(8 - n2),n∈ N n=1 or n=2 ( ∵ length should be +ve ) Hence required sum =2(8 - 12 + 8 - 22) =2× 11=22

Q. Find the sum of square of the length of the chords intercepted by the line $x + y = n; n \in N$ on the circle $x^{2} + y^{2} = 4$ .

$A B = 2 A M$
$A B^{2} = 4 A M^{2}$
$4 (4 - \frac{n ^{2}}{2}) = 2 (8 - n^{2}), n \in N$
$n = 1$ or $n = 2$ ( $∵$ length should be $+ v e$ )
Hence required sum
$= 2 (8 - 1^{2} + 8 - 2^{2})$
$= 2 \times 11 = 22$

Q. Find the sum of square of the length of the chords intercepted by the line x+y=n;n∈N on the circle x2+y2=4 .

AB=2AM AB2=4AM2 4(4−2n2​)=2(8−n2),n∈N n=1 or n=2 ( ∵ length should be +ve ) Hence required sum =2(8−12+8−22) =2×11=22

Q. Find the sum of square of the length of the chords intercepted by the line $x + y = n; n \in N$ on the circle $x^{2} + y^{2} = 4$ .

$A B = 2 A M$
$A B^{2} = 4 A M^{2}$
$4 (4 - \frac{n ^{2}}{2}) = 2 (8 - n^{2}), n \in N$
$n = 1$ or $n = 2$ ( $∵$ length should be $+ v e$ )
Hence required sum
$= 2 (8 - 1^{2} + 8 - 2^{2})$
$= 2 \times 11 = 22$