JEE PYQ: Circle Question 24
Question 24 - 2019 (08 Apr Shift 1)
The sum of the squares of the lengths of the chords intercepted on the circle, $x^2 + y^2 = 16$, by the lines, $x + y = n$, $n \in \mathbb{N}$, where $N$ is the set of all natural numbers, is:
(1) $320$
(2) $105$
(3) $160$
(4) $210$
Show Answer
Answer: (4)
Solution
Length of chord for line $x + y = n$: $L^2 = 4(16 - n^2/2) = 64 - 2n^2$. Need $n^2/2 < 16$, i.e., $n \le 5$. Sum $= \sum_{n=1}^{5}(64 - 2n^2) = 5 \times 64 - 2 \times 55 = 320 - 110 = 210$.
BETA
