g353x12:

The equation of an ellipse is x^2/a^2+y^2/b^2=1

where 2a and 2b are the lengths of the major and minor axis, respectively. Write a program in a script file that first derives the equation (symbolically) of the tangent line to the ellipse at the point (x_0,y_0) on the upper part of the ellipse (i.e. for -a<x_0<a and 0<y_0). Then, for specific values of a, b, x_0, and y_0 the program makes a plot, like the one shown on the right, of the ellipse and the tangent line. Execute the program with a=10, b=7, and x_0=8

I have no idea where to even start with this one...

Or this one:

g354x17:

A ceramic tile has the design shown in the figure. The shaded area is painted red and the rest of the rile is white. The border line between the red and the white areas follows the equation: y=Asin(pi/15*x)

Determine A such that the area of the white and red colors will be the same.

The picture below shows the shaded area. A square area of 15 inches by 15 inches with a positive sinusoidal curve taking up a certain percentage. The shaded area under the curve is supposed to equal the unshaded area inside the 15 x 15 inch square.

|------------

|----___-----

|---/----\----

|--/------\---

|-/-eqy----\--

|/----------\-

Thanks for any help!