JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The sum of the squares of the lengths of the chords intercepted on the circle, \(x^2 + y^2 = 16\), by the lines, \(x + y = n\), \(n \in N\), where \(N\) is the set of all natural numbers is
- A \(320\)
- B \(160\)
- C \(105\)
- D \(210\)
Answer & Solution
Correct Answer
(D) \(210\)
Step-by-step Solution
Detailed explanation
\(p = \frac{n}{{\sqrt 2 }}\), but \(\frac{n}{{\sqrt 2 }} < 4 \Rightarrow n = 1,2,3,4,5\) Length of chord \(AB = 2\sqrt {16 - \frac{{{n^2}}}{2}} \) \( = \sqrt {64 - 2{n^2}} = \ell \) (say) For \(n = 1,{\ell ^2} = 62\) \(n = 2,{\ell ^2} = 56\) \(n = 3,{\ell ^2} = 46\)…
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