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You are not logged in. #1 20130117 01:36:38
Represent the following equation as a hyperbola'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20130117 02:40:12
Re: Represent the following equation as a hyperbolaHi Agnishom, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #3 20130117 02:57:58
Re: Represent the following equation as a hyperbolaHi; and then replacing x1 by x1+ √2. You might download this http://math.sci.ccny.cuny.edu/document/show/2685 rename the file to Rotation of Axes.pdf This will explain some of this, won't make you as good as scientia or bob bundy with these transformation problems but it is a start. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #4 20130117 03:23:29
Re: Represent the following equation as a hyperbolahi bobbym So we now have a more familiar XY = 0 (the rectangular hyperbola) Now substitute* X = x/a  y/b and Y = x/a + y/b * substitutions like these preserve the hyperbolic nature of the curve. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #5 20130117 05:50:47
Re: Represent the following equation as a hyperbolaIn questions of this sort I tend look for a transformation to get rid of the term: When this is substituted into the original equation, the term in is We want this to vanish, so any such that and will do. So we take . Hence Thus under the transformation the curve becomes the hyperbola . Furthermore as the transformation represents a clockwise rotation of 45° about the origin followed by an enlargement of at the origin, the conic section is preserved, i.e. the original curve is indeed a hyperbola. NB: Be careful when using linear transformations on curves: only rotations, reflections and enlargements/contractions by a nonzero factor preserve conic sections. Any other transformation may distort the curve and alter its original nature. #6 20130117 12:59:21
Re: Represent the following equation as a hyperbolaOk thanks 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda 