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Chapter 11: Q. 4 (page 772)

Graph the equation: $x^{2} + 4 y^{2} = 4$

Short Answer

Expert verified

The graph of $x^{2} + 4 y^{2} = 4$ is

Step by step solution

01

Step 1. Given data

The given equation is

$x^{2} + 4 y^{2} = 4$

02

Step 2. Properties of equation

Rearrange the equation into the standard form of the equation of the ellipse

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

then

$a = 2 b = 1 c = \sqrt{a^{2} + b^{2}} c = 1.73$

vertices are $(\pm a, 0) = (\pm 2, 0)$

foci are $(\pm c, 0) = (\pm 1.73, 0)$

co-vertices are $(0, \pm b) = (0, \pm 1)$

03

Step 3. Graph

Plot a hyperbola of the vertices $(\pm 2, 0)$ ,co-vertices $(0, \pm 1)$ , and foci $(\pm 1, 0)$ to plot the graph of $x^{2} + 4 y^{2} = 4$

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Most popular questions from this chapter

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{matrix} x - y = 3 \\ \frac{1}{2} x + y = 3 \end{matrix} x = 4, y = 1; (4, 1)$

If a system of equations has no solution, it is said to be _______.

The product of two numbers is $10$ , and the difference of their squares is $21$ . Find the numbers.

The Tortoise and the Hare: In a 21-meter race between a tortoise and a hare, the tortoise leaves 9 minutes before the hare. The hare, by running at an average speed of 0.5 meter per hour faster than the tortoise, crosses the finish line 3minutes before the tortoise. What are the average speeds of the tortoise and the hare?

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$2 x + y - 3 z = 0 - 2 x + 2 y + z = - 7 3 x - 4 y - 3 z = 7$

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