Question

Conside the curve with parametric equations:

x=4t^2-5, y=2t+3

dy/dx, the equation of the tangent line when t=2, and the point(s) where there is a vertical tangent line

Answer 1

dy/dx=2/8t = 1/4t

Answer 2

do we need coordinates to find the equation of the tangent line or do we plug the value of t into the original x and y equations to find the x and y coordinates

Answer 3

You can plug in t. Thats the point of generalizing a derivative to handle parametrically defined curves.

Answer 4

yes i understand that part now but how do i find the points where there is a vertical line when y=0?

Answer 5

You mean, where is there a vertical line? Wherever the denominator is undefined. Namely, t=0. So the point would be:
(-5,3)

Answer 6

i dont see how you got that...

Answer 7

oh so we plug 0 into the original equations.....okay sorry slow moment THANKS MALEVOLENCE!!

Answer 8

Haha, its okay :P No problem xD