Question: how to find the slope of a tangent line to an ellipse?
Answer: Find the equation of the tangent and normal to the ellipse x2a2+y2b2=1 at the point (acosθ,bsinθ).
Let m be the slope of the tangent at the given point (acosθ,bsinθ), then. ... 
The equation of the tangent at the given point (acosθ,bsinθ) is.
This is the equation of the tangent to the given ellipse at (acosθ,bsinθ).