Having A little Trouble with this problem

• Dec 8th 2008, 05:45 PM
Zapz
Having A little Trouble with this problem
First of hello all.

This problem has me a little stumped, however I could just be over-thinking it like I usually do.

Here it is:

"Find the equation of the one line (there are two) tangent to the curve y^2 - xy + x^2 = 7 when x=1."

I found the derivative to be :
dy/dx = (y-2x)/(2y-x)

And From here I'm not quite sure where to go.

Can someone point me in the right Direction?

Thanks a billion
-Zapz
• Dec 8th 2008, 06:23 PM
tester85
Since you have found dy/dx, you are almost there you just have to find the y values

What you have to do is to substitute x=1 into y^2 - xy + x^2 = 7 and solve the quadratic equation. Then you will get two values for y. Which will be y = 3 or y = -2

All you have to do is to substitute y = 3, x = 1 into dy/dx and find the gradient and find the equation of the line.

Subsequently you can also substitute y = -2, x = 1 into dy/dx and find the gradient and find the equation of the line.

Just do one as the question requires to find only one equation of the line.

Hope it helps.

Quote:

Originally Posted by Zapz
First of hello all.

This problem has me a little stumped, however I could just be over-thinking it like I usually do.

Here it is:

"Find the equation of the one line (there are two) tangent to the curve y^2 - xy + x^2 = 7 when x=1."

I found the derivative to be :
dy/dx = (y-2x)/(2y-x)

And From here I'm not quite sure where to go.

Can someone point me in the right Direction?

Thanks a billion
-Zapz