Let `A(-4,0)` and `B(4,0)`. Then the number of points `C = (x,y)` on the circle `x^(2) +y^(2) = 16` lying in first quadrant such that the area of the triangle whose vertices are A,B and C is a integer is

Answer

62

Explanation

Required area
`A =(1)/(2)xx8xx|4 sin theta|= | 16 sin theta |`
Now, the area is an integer. Then the possible values of `sin theta` are
`(1)/(16),(2)/(16),.....,(15)/(16)`
i.e., 15 points in each quadrant or `60+2` more with `sin theta =1`.
Therefore,` N =62` lt