The sum of the square of the length of all the possible chords intercepted by the line x + y = n, for some n(belongs to N) on the circle x2 + y2 = 4 is what?
-
UP 0 DOWN 0 0 6
6 Answers
1Sir, I got the answer as (2√2)2 + (7)2 = 57.
However, the options are 11 or 22 or 33 or 48.
Please help.
62The sum of the square of the length of all the possible chords intercepted by the line x + y = n, for some n(belongs to N) on the circle x2 + y2 = 4 is what?
nikhil, what is the length of the chord when n=0?
and n=1, or n=2??
for other values of n, will it hit the chord
I think you have not understood the question correctly!
1For x + y = 1, square of length of chord is 14[points are {-(-1 + √7)/2, (1 + √7)/2)} and { (1 + √7)/2, -(-1 + √7)/2}]
For x + y= 0, square of length of chord is 16.[it is a diameter)
For x + y = 2, square of length of chord is 8[points are (2,0) and (o,2)].
So my answer comes out to be (14 + 16 + 8)=38.
However, the answer is 11 or 22 or 33 or 48. What to do, sir?
62Nikhil
sorry I completely missed this question
see closely.
Is the diameter of the circle 4 or 16?!