The Elements of Analytical Geometry Elements of the Differential And Integral
The Elements of Analytical Geometry Elements of the Differential And Integral
Elias Loomis
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Ex. 1. Transform the equation x^+y'^ = ^ from rectangular to polar co-ordinates. Ans. P'^{GOS. ^0 + sin. ^6) = 9, or p — 3. Ex. 2. Transform the equation xy=4: from rectangular to polar co-ordinates. JVote. Sin. 26=2 sin. Cos. (Trig. , Art. 73). Ans. P"" sin. 20=8. Ex. 3. Transform the equation x^-\-y'^=7nx from rectangular to polar co-ordinates. Ans. P=7n cos. 0. Ex. 4. Transform the equation x'^—y'^ = S from rectangular to polar co-ordinates. JVote. Cos. 20= COS. '0 - sin. '6 (Trig. , Art. 73...). Ans. P"" COS. 20=3. 68. To transform an equation from oblique to rectangular axes, find the values of x' and y^ from the formulas of Art. 56. To transform an equation from polar to rectangular co-ordi- nates, deduce the values of p and 9 from the equations of Ai-t. 57. These values are y — b and tang. 0=^ . X — cc THE CIRCLE. 69 SECTION lY. THE CmCLE. 59. Definition. A circle is a plane figure bounded by a line, all the points of which are equally distant from a point within called the centre.
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