# Find direction of tangent line to equation

1. Jan 29, 2012

### ArcanaNoir

1. The problem statement, all variables and given/known data

Find the direction of the line tangent to the curve $x^4+y^4=32$ at the point $(2, -2)$

2. Relevant equations

Anything goes, we're in vector calculus now.

3. The attempt at a solution

So, to find the tangent line, I was thinking of taking the gradient, but I'm not sure how to do that since the curve is in a squirrely format. I think they call that "implicit".

Perhaps the gradient is $4x^3i+4y^3j$?

and then at the given point we would have $32i-32j$

Is this actually the direction of the line tangent to the curve at the given point? Is this actually the answer? I don't really know.

2. Jan 29, 2012

### SammyS

Staff Emeritus
No. $32\hat{i}-32\hat{j},,$ is the direction of greatest slope. The tangent line is perpendicular to this.

3. Jan 29, 2012

### ArcanaNoir

darn. so how do I find the perpendicular to that?

4. Jan 29, 2012

### SammyS

Staff Emeritus
Rotate the vector 90°.

5. Jan 29, 2012

### Staff: Mentor

Remember doing lines perpendicular to a line how did you figure out the slope?

Negative inverse right?