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
y=-50 + 30 cos t ?
Guys, can someone please give me a step by step way to do this problem? I am very confused.
Thanks!!!!
eliminate t:
(30-x)/40 = (50+y)/30
30(30-x) = 40(50+y)
900-30x = 2000+40y
30x+40y = -1100
3x+4y = -110
x = 4n+2
y = -(3n+29)
Now just work out how many values of n produce x and y in the desired interval.
I think it is 9. Am I right?
It is saying it is wrong where have i messed this up?
well, let's see
n x y
23 94 -98
22 90 -95
...
-22 -86 37
-23 -90 40
-24 -94 43
-25 -98 46
Looks like a lot more than 9 to me.