Find the equation of the tangent line to the graph

In summary, the equations given are examples of implicit differentiation problems and the solutions are provided in the conversation. The equations are solved using implicit differentiation and the solutions are checked for accuracy.
  • #1
gillgill
128
0
i just want to check my answers...coz i don't have an answer key to compare with...
1) y^2-3xy+x^2=7
y'=3y-2x/2y-3x

2) x^2+y^2=2xy
y'=1

3) 2x^2+xy+3y^2=0
y'=-4x-y/x+6y

4) 5x^2-2xy+7y^2=0
y'=y-5x/7y-x

5) 7x^2+6xy+9y^2=0
y'=-7x-3y/3x+9y

6) Find the equation of the tangent line to the graph of x^2+2y^2=3 at (1,1)
ans: x+2y-3=0

7) Find the equation of the tangent line to the graph of x^2+3y^2=4 at (1,1)
ans: x+3y-4=0

are those correct?
Thanks for your time
 
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  • #2
I'd look over those if they were latexed.. :P
Thats too messy, but just integrate them and see if you get the original function.
 
  • #3
I checked number 6, and it is correct, so I assume no. 7 is probably correct too.

I have no idea what the questions were for 1 to 5, so can't help you there.
 
  • #4
Theyre implicit differntiation problems. I'll do #2:

2) x^2+y^2=2xy

2x + 2yy' = 2y + 2xy'

2x - 2y = 2xy' - 2yy'

2x-2y = y'(2x-2y)

y' = 1
 

Related to Find the equation of the tangent line to the graph

What is the equation of the tangent line to a graph?

The equation of the tangent line to a graph is a linear equation that represents the slope of a curve at a specific point. It can be written in the form y = mx + b, where m is the slope of the tangent line and b is the y-intercept.

How do you find the equation of the tangent line to a graph?

To find the equation of the tangent line to a graph, you will need to know the coordinates of the point where the tangent line intersects the curve. Then, you can use the slope formula (m = (y2-y1)/(x2-x1)) to calculate the slope at that point. Finally, you can plug the coordinates and slope into the slope-intercept form of a line (y = mx + b) to get the equation of the tangent line.

Can you find the equation of the tangent line to a graph without knowing the coordinates of the point?

No, in order to find the equation of the tangent line to a graph, you will need to know the coordinates of the point where the tangent line intersects the curve. Without this information, you cannot accurately determine the slope or the y-intercept of the tangent line.

Are there any special cases when finding the equation of the tangent line to a graph?

Yes, there are a few special cases when finding the equation of the tangent line to a graph. If the curve is a straight line, the equation of the tangent line will be the same as the equation of the curve itself. If the curve is a circle, the tangent line will be perpendicular to the radius of the circle at the point of tangency. Additionally, if the curve has a sharp corner or discontinuity at the point of tangency, the equation of the tangent line will not exist.

Why is finding the equation of the tangent line to a graph important?

Finding the equation of the tangent line to a graph is important because it allows us to determine the instantaneous rate of change of a curve at a specific point. This can be useful in many fields of science, such as physics and engineering, where knowing the slope at a certain point can help us make predictions or optimize systems. It also allows us to better understand the behavior and properties of the curve at that point.

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