Optical illusions-lines intersect a family of curves


Assignment:

Optical Illusions - finding dy/dx for different figures

Q: In each graph below, an optical illusion is created by having lines intersect a family of curves. In each case, the lines appear to be curved. Find the value of dy/dx for the given values of x and y for each of the below.

1) For Figure A below (the circles):

Circles: x2 + y2 = C2

x = 3, y = 4, and C = 5

2) For the hyperbolas (Figure B):

xy = C, x = 1, y = 4, C =4

3) For Figure C below:

Lines: ax = by
x = Square root of 3, y = 3
a = Square root of 3, b = 1

4) For Figure D below:

Cosine curves: y = C cos x
x = π/3, y = 1/3, C = 2/3

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312_Optics.jpg

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Mathematics: Optical illusions-lines intersect a family of curves
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