y2t= -(7/15)(3t+1)2 + 157/15
Find points of intersection and collision
The Attempt at a Solution
Well, to find the intersection I think I need to eliminate the parameters for both equations so I get an equations in terms of x and y, and then set them eqaul to each other.
using the rule cos^2+sin^2=1 and substituting, we get
((y-3)/7)^2 + ((2-x)/3)^2 = 1
I guess we should solve for y here?
Seems a little unwieldy to simplify; is there a trick or something?
Anyways, I used the solve function on my calc and got
y= (7*sqrt(-x^2 + 4x+5) +9) / 3
now on to the other curve
plug the equations for t into the y equation
I really don't know how to deal with this manually. the y2t function is complicated enough by itself, and now i have to replace t with a fraction.
I did however graph the function and i think maybe the answers are t=1 which is (5,3) and t=1/2 which is (2, 10)
not entirely sure.
and then for collision, we set the x functions to be the same?
I used a calc and got t= -1, -0.7898, 0.377
can the last two values be represented in fractional from with pi?
now i do the same thing w/ y functions
3+7sin(pit)= -(7/15)(3t+1)2 + 157/15
do i have to pretty much use a calculator for this?
anyways, i got t=-1.208, 0.307, 1, 1.52
none of the t values are the same.
in desperate need of help plz >.>