Lemniscate of Bernoulli - Information from Answers.com
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given
... r^2 = 2a^2 \cos 2\theta\, . As parametric equation: x = \frac{a\sqrt{2}\cos(t) ...
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Cassini oval - Information from Answers.com
They are the special case of polynomial lemniscates when the polynomial used
... r^4-2a^2r^2 \cos 2\theta = b ... (\pm a \sqrt{1-e^4}, 0): (0, \pm a \sqrt{e^4-1}) ...
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hyperbola: Definition from Answers.com
the distance r from a point (x\ ,\ y) ... Just as the sine and cosine functions give a
parametric equation for the ellipse, .... If the center of inversion is chosen as the
hyperbola's own center, the inverse curve is the lemniscate of Bernoulli; the
lemniscate is also .... These are equilateral hyperbolas (eccentricity \varepsilon =
\sqrt 2 ) ...
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analytic geometry: Definition from Answers.com
The equation x2 + y2 = r2 is the equation for any circle with a radius of r. ... d = \
sqrt{(x_2 - x_1)^2 + (y_2 - .... We then solve the remaining equation for x, in the
same way as in the substitution method. x2 -2x +1 +1 -x2 =1 -2x = -1 x=½ We next
place ..... Involute (geometry); Lemniscate of Bernoulli (geometry); Linear algebra ...
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