parameteic equation maths -II

[deviany]

a particle P moves in a plane so that at time t its coordibates are given x=4cost, y=3sint
the qs asked me to find the value of t for which the particle is travelling parallel to the line x+y=0
i am very clueless to the nxt step like i tried to change my eq of tangent with y=-x... but still im.very clueless

 

[Cubist]

Have you been taught how to differentiate parametric equations?

 

[yoscar04]

By the way, I think you published twice the same problem.

 

[Deleted member 4993]

By the way, I think you published twice the same problem.

This problem is somewhat similar to:

please help parameteic equation maths

number 9 part 2 and 3. if its parallel to x axis then the gradient would be 0. but how can i proof it? i triedy dy/dx=0 but i got t=2... which part i am wrong?

www.freemathhelp.com

But not quite the same.

 

[yoscar04]

Rotated...

 

[HallsofIvy]

If x=4cos(t), y=3sin(t). Then dx/dt= -4sin(t), dy/dt= 3cos(t). The slope of the tangent line is dy/dx= (dy/dt)/(dx/dt). The line x+ y= 0 is the same as y= -x so has slope -1. The tangent line will be parallel to x+ y= 0 when dy/dt= (3 cos(t))/(-4 sin(t))= -1 so when 3 cos(t)= 4 sin(t). That, of course, is the same as sin(t)/cos(t)= tan(t)= 3/4.