Analytic Geometry for Technical Schools And Colleges

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Let the pole A' referred to the rectangular coordinates be (m, n), 6' the angle made by the polar axis with the X-axis. Then X = AD = m + r cos (6 + 6'), y = PD = n + r sin (d + 6').
When the pole is at the origin, and the polar axis coincides with the X-axis, these formulas be- come X = r cos 6, y — r sin $.
If the polar equation of a geometric figure is given and the rectangular equation is desired, find the values of the polar coordinates r and 6 of any point in terms of the rectan- 80 ANALY
...TIC GEOMETRY gular coordinates x and y of the same point ; substitute in the polar equsition F(r, 6) = 0, and the resulting equation /(a;, ?/)=:0 is the rectangular equation of the curve. From the figure X — m r = y/{x - my +{y- w)^ cos (6 + 6') = sin(^ + ^')- •'~'" ^{x - mf + (2/ - ?0' V(. X'-m/+(y-n)^ When the origin is at the pole, and the X-axis coincides with the polar axis, these formulas become r — V. V- + ]j\ cos Q = ^ sin 9 = • VaT- + y- Var + y- Problems. — Transform from rectangular coordinates to polar, pole at origin, polar axis coinciding with A'-axis, and plot the locus from both equations.

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