Question

View the curve (y-x)^2 + 2 = xy - 3 as a contour of f(x,y).
a) Use \nabla f (2,3) to find a vector normal to the curve at (2,3).


(b) Use your answer to part (a) to find an implicit equation for the tangent line to the curve at (2,3).

Answer 1

a is <-5,0> but what is b

Answer 2

I think the vector perpendicular to a= < -5,0> is b= <0,5>
a dot b =0 (as a check)

a line through point <2,3> would be P= <2,3>+t<0,5>
where P is a position vector, and t is a scalar

Answer 3

It looks like the "direction vector" <0,5> points straight up, so an equivalent equation is
x=2

Answer 4

Here is a graph of the scenario
(see geogebra.org to download this software)