It says to find the equation of a tangent line with a slope of m = $\frac{-2}{9}$ to ellipse $4x^2+9y^2=40$.
I have y' = $\frac{-4x}{9y}$. I don't understand what to do next. How can I find the values of x and y?
[Math] How to find tangent of ellipse with slope
calculus
Best Answer
Hint:
Compare both the slopes, you get: $$2x=y$$ As this point $(x,y)$ must lie on the ellipse, Use that $$4x^2+9y^2=40$$ $$\implies 4x^2+9(2x)^2=40$$ Solve for $x$ and then find $y$,
You now have $(x,y)$ , the point of tangency, now you can write the equation of the tangent.
(You have it's slope and $1$ point lying on it)