Is my equation of the tangent line at (2,-1) correct?

In summary, the conversation is about finding the equation of the tangent line to the curve x^3-2x^2y+y^2=17 at the point (2,-1). The initial attempt to find the equation resulted in a sign error in the derivative. After correcting the error, the final equation for the tangent line is y+1=(-1/4)(x-2). However, there is still an issue with the exponent and coefficient in the derivative, so the individual is advised to double check their work.
  • #1
excelsion
13
0
i would like to know if my answer is correct can someone tell me the results for this:
Find the equation of the tangent line to x^3-2x^2y+y^2=17 at (2,-1)

ive gotten y'=(3x^2+4xy)/(-2x^2-y)
and my line equations is
y+1=(-1/4)(x-2)
thanks in advance
 
Last edited:
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  • #2
I think you have some sign problems in your derivative. Check again.
 
  • #3
i did it wrong i re did it and got this:
dy/dx=-3x^2+4xy^2/-4x^2+2y

is that correct?
 
  • #4
The signs have improved, but you have bad exponent in the numerator and a bad coefficient in the denominator. I think if you do it once more carefully, you'll get it.
 

What is the equation of a tangent line?

The equation of a tangent line is a straight line that touches a curve at only one point and has the same slope as the curve at that point.

How do you find the equation of a tangent line?

To find the equation of a tangent line, you need to know the slope of the curve at the point of tangency and the coordinates of that point. You can use the point-slope form of a line to create the equation.

What is the point-slope form of a line?

The point-slope form of a line is y - y1 = m(x - x1), where (x1,y1) is a point on the line and m is the slope of the line.

How do you find the slope of a curve at a specific point?

The slope of a curve at a specific point is equal to the slope of the tangent line at that point. You can find the slope using the derivative of the curve at that point.

Can you find the equation of a tangent line at any point on a curve?

Yes, you can find the equation of a tangent line at any point on a curve as long as you know the slope of the curve at that point and the coordinates of the point. However, some curves may have vertical tangent lines, which do not have a defined slope. In this case, the equation of the tangent line cannot be found using the standard methods.

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