# Thread: Having A little Trouble with this problem

1. ## 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

2. 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.

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