Home Work Problem Set # I

MATHEMATICAL REPRESENTATION OF GEOMETRICAL ELEMENTS

1. Consider an equation of a set of lines f(x, y, t) = tx + (1-t)y + t(t-1) = 0

Find the equation of the envelope to these lines in implicit and parametric form.

2. Show that for a line P0P1, the implicit form is equivalent to the parametric form.

3. Find the tangent to a circle x2 + y

2 = 1 at (1, 0). What problem do you face? Can you find the

tangent to the circle if you convert the equation of the circle in explicit form? Show. What

would be the equation of the normal in the explicit form? Would you have some problems

with the finding of normal to the circle? Justify your answer.