Equation of a Tangent Line to a Polar Curve

[zmilot]

I need to find the equation of the tangent line to the curve

x=t⁴+1, y=t³+t; t=-1

I have already found that the slope of the line is -1 by finding (dy/dt)/(dx/dt) I just need to figure out how to solve for y₁ and x₁

Thanks in advance

 

[micromass]

Hi zmilot!

I need to find the equation of the tangent line to the curve

x=t⁴+1, y=t³+t; t=-1

I have already found that the slope of the line is -1 by finding (dy/dt)/(dx/dt) I just need to figure out how to solve for y₁ and x₁

Thanks in advance

So you've got the slope of the tangent line, that's good. Can you find a point on the tangent line?? If you have the slope and any point, then you can easily find the equation with certain formulas.

 

[zmilot]

Thats what I was trying to figure out, how do you find a point on the tangent line, all I have is the slope and I don't know where they intersect

 

[micromass]

Thats what I was trying to figure out, how do you find a point on the tangent line, all I have is the slope and I don't know where they intersect

What's the intersection of the tangent line with the curve?

 

[zmilot]

The only way I know to find the intersection is to set the equations equal to each other, but since I don't have the tangent line equation I am not sure how to go about this.

 

[ArcanaNoir]

When t=-1, what is x? What is y? is this the point for which you calculated the derivative?

 

[zmilot]

I don't think they line intersects at t=-1, that was just the number we were given to plug into the first derivative in order to find the slope. I am really lost on this problem so if anyone could make sure my first step is right and then walk me through the rest of the process it would be greatly appreciated.

 

[ArcanaNoir]

You found the tangent line to the point at which t equals negative one. I wasn't really asking a question so much as inviting you to see it.

 

[micromass]

You're taking the tangent line of the curve at t=-1. What does that mean?