Thread: Tangent at point...

Ok so i was assigned some math problems over the summer but lost my math binder from last year and i dont remember how to solve this:

x^2 -xy + y^2 = 9
Find the point at which a vertical tangent exists

I remember i used to be able to solve this so its really frustrating i forgot how... Just need a little help remembering. Thanks

Originally Posted by ijleyton

Ok so i was assigned some math problems over the summer but lost my math binder from last year and i dont remember how to solve this:

x^2 -xy + y^2 = 9
Find the point at which a vertical tangent exists

I remember i used to be able to solve this so its really frustrating i forgot how... Just need a little help remembering. Thanks

steps:

- differentiate implicitly
- solve for dy/dx
- vertical tangents occur when dy/dx is undefined. solve for this

Ok so i did:

x^2 -xy + y^2 = 9
2x - x(dy/dx)*y + 2y(dy/dx) = 0
Now if i continue solving for this i would get an 'x' and a 'y' in my answer.. How do i fix that? :s
-This used to be really easy.. the summer made me rusty

Originally Posted by ijleyton

Ok so i did:

x^2 -xy + y^2 = 9
2x - x(dy/dx)*y + 2y(dy/dx) = 0
Now if i continue solving for this i would get an 'x' and a 'y' in my answer.. How do i fix that? :s
-This used to be really easy.. the summer made me rusty

rusty indeed, you differentiated incorrectly (you need the product rule to differentiate -xy)

the actual answer is

now solve for dy/dx

you will get a rational function. these are undefined where the denominator is zero (provided the numerator isn't zero at the same time). so set it equal to zero and solve for y. once you have y, plug it into the original equation and solve for x. this will give you the vertical lines you seek. they are of the form x = something of course

haha i feel really stupid for not being able to figure this out
Ok so i have:
2x-y-x(dy/dx) -2y(dy/dx)=0
i tried to isolate (dy/dx) and was left with:
(dy/dx)= (2x+y)/(x+2y)
Now if i understood you correctly you wanted me to set (x+2y)= 0
That would mean 2y=-x ... now what?
-The answer choices have radicals.. i dont see how i'm gonna get that

Originally Posted by ijleyton

haha i feel really stupid for not being able to figure this out
Ok so i have:
2x-y-x(dy/dx) -2y(dy/dx)=0
i tried to isolate (dy/dx) and was left with:
(dy/dx)= (2x+y)/(x+2y)
Now if i understood you correctly you wanted me to set (x+2y)= 0
That would mean 2y=-x ... now what?
-The answer choices have radicals.. i dont see how i'm gonna get that

i told you exactly how to finish the problem

i got

set , plug this in for y in the original, we get:





solve that to get your (radical) solutions