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Nookie1986 [14]
3 years ago
9

Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equat

ions. Use arrows to show the orientation of the curve corresponding to increasing values or t.
x=2cost,y=3sin t,0≤t<2π

Mathematics
1 answer:
____ [38]3 years ago
4 0

Answer:

9x^2+4y^2=36

Step-by-step explanation:

We are given that

x=2cos t

y=3 sin t

0\leq t\leq 2\pi

cost=\frac{x}{2}

sint=\frac{y}{3}

sin^2 t+cos^2 t=(\frac{x}{2})^2+(\frac{y}{3})^2

1=\frac{x^2}{4}+\frac{y^2}{9}

By using the formula

sin^2\theta+cos^2\theta=1

1=\frac{9x^2+4y^2}{36}

9x^2+4y^2=36

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