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Geometry Level pending

What type of curve do these parametric equations represent?

x = − 1 8 cos ⁡ ( 2 t ) + 15 8 sin ⁡ ( 2 t ) x = -\frac{1}{8}\cos(2t)+\frac{\sqrt{15}}{8}\sin(2t)

y = 1 8 sin ⁡ ( 2 t ) + 15 8 cos ⁡ ( 2 t ) y=\frac{1}{8}\sin(2t)+\frac{\sqrt{15}}{8}\cos(2t)

( − ∞ < t < ∞ ) (-\infty<t<\infty)

Circle Rose Curve Lissajous Curve Lemniscate

James Wilson by James Wilson , 28, USA

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1 solution

Hongqi Wang
Jan 16, 2021

x 2 + y 2 = ( − 1 8 cos ⁡ ( 2 t ) + 15 8 sin ⁡ ( 2 t ) ) 2 + ( 1 8 sin ⁡ ( 2 t ) + 15 8 cos ⁡ ( 2 t ) ) 2 = 1 4 x^2 + y^2 \\ = (-\dfrac 18 \cos(2t) + \dfrac {\sqrt {15}}8 \sin(2t))^2 + (\dfrac{1}{8}\sin(2t) + \dfrac{\sqrt{15}}{8}\cos(2t))^2 \\ = \dfrac {1}{4}

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