CIRCLES

just make a circle , u see there are 13 points on the axis and 8 points lie in a single quadrant nd there are 4 quadrants so there is a total of 32 points in all the 4 quadrants . so sum of all points is 32 + 13 = 45

3. in third ques first find the eq of that line nd then find the point of intersection P and Q , nad then accc to the given condition find alfa and beta and put then in the eq as ; x² + ( alfa + beta ) x + (alfa)(beta) = 0

@Ajoy, May you please tell wherefrom are these sums taken?

2nd isnt difficult,
the outermost mod has no meaning , just remove it
now u hav to take cases

1] x≥2 , y ≥1

2] x≥2 , y < 1

3] x≤ 2 y ≥ 1

4] x≤2 , y < 1

for 3rd , line AB is y = 2x - 2

solve this line wid the circle , and get 2 pts P (0, -2 ) and Q (8/5 , 6,5 )

so u get PB , AP , BQ, AQ, and thus alpha and beta,

and then eqn will be (x - α) ( x - β) = 0

for 4th , wont it depend on the given circles ? it can be an ellipse if one circle lies inside other and are non concentric , it will be a circle for 2 concentric circles, etc etc

q1
refer to the link http://en.wikipedia.org/wiki/Pick's_theorem