Tangent to an Ellipse given the slope of the tangent

[Liz226]

Homework Statement

Determine the points on the ellipse x^2 a 2y^2=1 where the tangent line has a slope of 1

Homework Equations

I'm able to solve problems when given points and asked to find equations of the tangent lines. However, I'm struggling to do the inverse.

The Attempt at a Solution

I've set up the ellipse in an implicit grapher and played around with it to try to find approximately what points it would be, and haven't had much luck, seeing as the implicit graphers don't allow for tracing and such. Setting the equation as y=1x+b seems to be the logical first action; however, I have no clue where to go from there.

Any and all help would be greatly appreciated

 

[Dick]

Use implicit differentiation to express y' as a function of x and y. Then set y'=1. What kind of a condition does that give you on x and y?

 

[Liz226]

2x+4y(dy/dx)=1
4y(dy/dx)=1-2x
(dy/dx)=(1-2x)/(4y)