Hello hciR Originally Posted by

**hciR** Hi, I have to find the co-ordinates where the line y=-x+1 intersects f(x,y) = x^2 + y^2 -xy - y -1

I can do this with explicit functions by making them equal, but it doesn't work with this.

The actual question asks for the co-ordinates where the tangent to f(x,y), is at 45 deg to the horizontal. So I found the gradient function which = 1 (that got me the linear equation), now i'm stuck.

Not sure if this should be in calc. section, so sorry if I got it wrong.

Thanks, Rich.

I assume that the curve is $\displaystyle f(x,y)=0$, in which case I agree that $\displaystyle y = 1-x$ when $\displaystyle \frac{dy}{dx}=1$.

Just substitute $\displaystyle y = 1-x$ into $\displaystyle f(x,y)=0$ to eliminate $\displaystyle y$, and solve the resulting quadratic in $\displaystyle x$. I make the answer

$\displaystyle x=-\tfrac13, \;1$

Then find the corresponding values of $\displaystyle y$.

Grandad