Suppose that a trammel's grooves are tilted, so that the slider farthest from the handle moves...

  

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Suppose that a trammel's grooves are tilted, so that the slider farthest from the handle moves allong the x-axis, but instead of moving allong the vertical axis, the near slider has position (mu, u) for some value of u with m 0. a. Find a system of implicit equations for this trammel's mobility without using trigonometry. b. Use the observation that the two screws are always distance s apart to parameterize u and p as linear functions of cos(t) and sin(t)) for a new parameter t being the angle between the horizontal groove and the handle measured on the left side. c. Thinking geometrically about the meaning of the free parameter t, use your parameterization of u(t) and p(t) to express x and y as functions of free variable t, and the system parameters. d. Use this parameterization to show that the handle still traces an ellipse for all slopes m + 0. Suppose that a trammel's grooves are tilted, so that the slider farthest from the handle moves allong the x-axis, but instead of moving allong the vertical axis, the near slider has position (mu, u) for some value of u with m 0. a. Find a system of implicit equations for this trammel's mobility without using trigonometry. b. Use the observation that the two screws are always distance s apart to parameterize u and p as linear functions of cos(t) and sin(t)) for a new parameter t being the angle between the horizontal groove and the handle measured on the left side. c. Thinking geometrically about the meaning of the free parameter t, use your parameterization of u(t) and p(t) to express x and y as functions of free variable t, and the system parameters. d. Use this parameterization to show that the handle still traces an ellipse for all slopes m + 0.