number of points having integral co-ordinates and satisfying x2+y2≤5 is
1. 14
2. 21
3. 20
4. none of these
please give a detailed solution.
P.S.- nishant sir, i want a solution to this asap.
1(2) 21
we need to find the number of "integral" points on or inside the circle centered at origin and having radius of √5 ≈ 2.3.
as this is a symmetrical figure you can do this just by a rough plot.
also one thing which is very handyin these type of questions is that the number of "integral" points can only be of the form '4n+1'.
1draw a circle with the centre at the origin with radius √5 as rishabh had rightly mentiond..
i am nt dat good in drawing so i`l explain what i`ve done..
first,u knw radius less than 2.3....so find out the integral pnts on the x and the y axes which will be:
(2,0),(1,0),(-2,0),(-1,0),(0,0),(0,2),(0,-2),(0,1),(0,-1)....so 9 pnts in total
now find the value of y co-ordinate on the circle corresponding to the x co-ordinates 1 and 2..
so corrspnding to 1 y co-ordinate is 2 and crrspndng to 2 y is 1....so lyk this u`l get the co-ordinates as:(1,2),(1,-2),(-1,2),(-1,-2),(1,1),(2,1),(-2,1),(2,-1),(-2,-1),(1,-1),(-1,1),(-1,-1)..total 12pnts
so 21 pnts in all....seems to be long,this method on paper but it dsnt` take long to think
