Asked by Bob

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!!!!
Answered by Steve
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.
Answered by Bob
I think it is 9. Am I right?
Answered by Bob
It is saying it is wrong where have i messed this up?
Answered by Steve
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.
Answered by Steve
Oops. Not all of those are <u>on</u> the graph. You may be right.
Answered by Dr. Legit
Actually, it's 21, to anybody out there who still needs this question answered.
Answered by Talia
Thank you Dr. Legit! that was very helpful
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