# How do you convert the parametric equation to rectangular form #x = e^t#, #y = e^(-t)#?

By signing up, you agree to our Terms of Service and Privacy Policy

To convert the parametric equations ( x = e^t ) and ( y = e^{-t} ) to rectangular form, solve for ( t ) in terms of ( x ) and ( y ), then substitute these expressions back into the equations to eliminate ( t ) and express ( y ) in terms of ( x ).

Solving for ( t ) in terms of ( x ) and ( y ):

- From ( x = e^t ), take the natural logarithm of both sides to get ( t = \ln(x) ).
- From ( y = e^{-t} ), take the natural logarithm of both sides to get ( -t = \ln(y) ). Multiply both sides by -1 to get ( t = -\ln(y) ).

Now substitute these expressions back into the original parametric equations:

- Substitute ( t = \ln(x) ) into ( y = e^{-t} ) to get ( y = e^{-\ln(x)} ).
- Simplify ( e^{-\ln(x)} ) to ( \frac{1}{x} ).

Therefore, the rectangular form of the parametric equations is ( y = \frac{1}{x} ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the arclength of #f(t) = (-(t+3)^2,3t-4)# on #t in [0,1]#?
- How do you differentiate the following parametric equation: # x(t)=t^2-te^t , y(t)=e^(3t) #?
- For #f(t)= (1/(t-3),t^2)# what is the distance between #f(0)# and #f(2)#?
- What is the arclength of #(e^(-2t)-t^2,t-t/e^(t-1))# on #t in [-1,1]#?
- How do you differentiate the following parametric equation: # x(t)=1/t, y(t)=1/(1-t^2) #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7