Question

can anyone help with this quesiton? its simmilar to the one i just asked.
suppose that a particles position is described by r(t)=3cos(t)i+5sin(t)j
Give an equation(in the form of a formula involving x and y set equal to 0)whose solutions consist of the path of the particle.
The answer looks like ____________=0
I solved it and got 3cos(arcsin(y/5))-x=0 but it is saying that it is wrong.

Answer 1

The formula describes an ellips

Answer 2

Now your job is to
a) Look up the IMPLICIT equation of an ellipse
b) Fit the specific case - to the general parameters

Answer 3

Google/wikipedia for ellipse

Answer 4

ok i know what the elipse equaton is
(x^2/a^2)+(y^2/b^2)=1

Answer 5

The equation of an ellipse whose major and minor axes coincide with the Cartesian axes is
\[\frac{ x^2 }{ a^2} + \frac{y^2}{b^2} = 1\]
This means any noncircular ellipse is a squashed circle. If we draw an ellipse twice as long as it is wide, and draw the circle centered at the ellipse's center with diameter equal to the ellipse's longer axis, then on any line parallel to the shorter axis the length within the circle is twice the length within the ellipse. So the area enclosed by an ellipse is easy to calculate-- it's the lengths of elliptic arcs that are hard.

Answer 6

Look at YOUR FORMULA - what should one change so that it will become an ellipse ?...

Answer 7

This is the connection to solution

Answer 8

Well yor Two parameters are a = 3 b = 5

Answer 9

ok so would it be (cos(x)^2/9)+(sin(y)^2/25)-1=0?