find tangent to ellipse

Dick Lane
Function f is a real-valued function of two variables: f(x,y) = (x/a)^2 + (y/b)^2 Each level-curve of f is an ellipse centered at the origin.
  • Shape depends on parameters a,b [use sliders to choose integer values between 1 and 9].
  • The ellipse will go thru point P --- move P to determine size of the ellipse.
Use suitable calculus ideas to find an equation for the line tangent to this ellipse at point P. Although that work will require knowing exact coordinates for P, it is not necessary to compute the value of function f there. Enter your equation using the (shaded) input box below the figure (press Return to view your line). Hint: implicit differentiation can simplify some computations.