How to find the tangent line to a curve given parametric equations?
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.
x = t − t^−1, y = 7 + t^2, t = 1
I am not sure how to go about this. Help is appreciated!
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.
x = t − t^−1, y = 7 + t^2, t = 1
I am not sure how to go about this. Help is appreciated!
1 Answer
Apr 29, 2018
Explanation:
You have to determine
Recall that
#dy/dx = (dy/(dt))/(dx/(dt))#
We know that
#dy/dx= (2t)/(1 + 1/t^2)#
The slope of the tangent line is given by evaluating
#m = (2(1))/(1 + 1) = 1#
Now find the values of
#x(1) = 1 - 1 = 0#
#y(1) = 1^2 + 7 = 8#
The equation will therefore be
#y - 8 = 1(x -0)#
#y = x + 8#
Hopefully this helps!