Chapter 10: Q. 3. (page 694)

The parametric equations $x = 2 \sin t, y = 3 \cos t$ define a(n)______.

Short Answer

Expert verified

The parametric equations $x = 2 \sin t, y = 3 \cos t$ define a(n) ellipse.

Step by step solution

Step 1. Given information.

The parametric equations $x = 2 \sin t, y = 3 \cos t$ are given.

Step 2. Fill the blank.

The parametric equation of an ellipse is defined as;

$x = a \sin (t), y = b \cos (t)$

After comparing the above equations from the given equations.

We get, $a = 2, b = 3$

Thus, the equation of an ellipse is written as,

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \Rightarrow \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$

The parametric equation defines a(n) ellipse because an ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.

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The parametric equations $x = 2 \sin t, y = 3 \cos t$ define a(n)______.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Fill the blank.

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Short Answer

Step by step solution

Step 1. Given information.

Step 2. Fill the blank.

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Most popular questions from this chapter

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The parametric equations $x = 2 \sin t, y = 3 \cos t$ define a(n)______.