The Elements of Analytical Geometry Elements of the Differential And Integral

Cover 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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