Engineering Calculus Notes 144

Engineering Calculus Notes 144 - equation y = x 2 whose...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
132 CHAPTER 2. CURVES x 2 4 + y 2 1 = 1 ( x +2) 2 4 + ( y 2) 2 1 = 1 Figure 2.10: Displacing an ellipse We can also refect a locus about a coordinate axis. Since our model ellipses and hyperbolas are symmetric about these axes, this has no e±ect on the curve. However, while the model parabola given by Equation ( 2.10 ) is symmetric about the y -axis, it opens up ; we can reverse this, making it open down , by replacing y with y , or equivalently replacing the positive coe²cient p with its negative. For example, when p = 1 this leads to the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: equation y = x 2 whose locus opens down : it is the refection o our original parabola y = x 2 about the x-axis (Figure 2.11 ). y = x 2 y = x 2 Figure 2.11: Refecting a parabola about the x-axis Finally, we can interchange the two variables; this eects a refection about the diagonal line y = x . We have seen the eect o this on an ellipse and hyperbola. For a parabola, the interchange x y takes the parabola...
View Full Document

This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online