Find the slope of the tangent line to the ellipse x^(2)/16 +y^(2)/4=1 at the point (x,y). slope =?

Question

Find the slope of the tangent line to the ellipse x^(2)/16 +y^(2)/4=1 at the point (x,y). slope =?

Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), (-2,5). Enter none if there are no such points.) slope is undefined at ?

Answer 1

The equation is an ellipse centered at the origin.

The slope at each point is -x/4y.

The slope is undefined when y=0, i.e. when x=±4.

This is where the ellipse crosses the x-axis and the tangent is, in fact, perpendicular to the x-axis.