Find the equation of the tangent line to the graph

[gillgill]

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

 

[whozum]

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.

 

[James R]

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.

 

[whozum]

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