A lattice point is a point with integer coordinates. How many lattice points (x,y) with -100 less than or equal to x less than or equal to 100 and -100 less than or equal to y less than or equal to 100 are on the graph of the parametric equations x=30-40 cos t and y=-50 + 30 cos t?

Answer 1

the graph is an ellipse

(x-30)/40 = -cos t
(y+50)/30 = sin t

(x-30)^2/1600 + (y+50)^2/900 = 1

the ellipse has semi-axes 30 and 40

Not sure how many lattice points lie on the curve. At least 8.