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Chapter 10: Q. 38 (page 695)

In Problems 35–38, find parametric equations that define the curve shown.

Short Answer

Expert verified

The parametric equation is $x = \cos t, y = 4 \sin t, 0 \leq t \leq \frac{π}{2}$

Step by step solution

01

Step 1. Given Information

We are given a graph

Given the curve and its coordinates, we were asked to determine its parametric equation. To do that, we have to find equation representing the given graph to find the parametric equation.

02

Step 2. Finding Parametric Equations

Here $a = 1, b = 4$

Thus, $x = \cos t y = 4 \sin t$

The given graph only shows half of the ellipse in a counterclockwise direction $0 \leq t \leq \frac{π}{2}$

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Most popular questions from this chapter

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

The directix of a line $y = - \frac{1}{2}$ and the vertex is at $(0, 0)$ .

In Problems 15–18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

$(A) \frac{x^{2}}{4} - y^{2} = 1 (B) x^{2} - \frac{y^{2}}{4} = 1 (C) \frac{y^{2}}{4} - x^{2} = 1 (D) y^{2} - \frac{x^{2}}{4} = 1$

Graph:

If $θ$ is acute, the Half-angle Formula for the sine function isrole="math" localid="1646654694239" $\sin \frac{θ}{2} =______$ .

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Vertex is at $(4, - 2)$ and focus is at $(6, - 2)$ .

Answer Problem using the figure.

If a = 4, then the coordinates of the focus are___________.

See all solutions

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