Tangent Line Transformations
نویسنده
چکیده
The new curve contains all of the information about the original curve’s tangent lines. For example, it crosses the y-axis whenever the original curve has a horizontal tangent line. The straight line y = mx + b, or (x(t), y(t)) = (t,mt + b), has only one tangent line and thus a trivial transformation to a point, (x∗(t), y∗(t)) = (m, b). Some conic sections transform to conic sections. For example, the image of the unit circle (x(t), y(t)) = (sin t, cos t) is (x∗(t), y∗(t)) = (− sin t cos t , cos t + sin t cos t · sin t ) = ( − sin t cos t , 1 cos t )
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