Chapter 11: Q. 183 (page 1135)

In the following exercises, graph each equation.
$16 x^{2} + 9 y^{2} = 144$

Short Answer

Expert verified

Graph of the conic represented by the equation is an ellipse.

Step by step solution

Step 1. Standard form of the equation,

$16 x^{2} + 9 y^{2} = 144 \frac{16 x^{2} + 9 y^{2}}{144} = \frac{144}{144} \frac{x^{2}}{9} + \frac{y^{2}}{16} = 1 \frac{x^{2}}{3^{2}} + \frac{y^{2}}{4^{2}} = 1$

Step 2. Key features of the graph,

Equation of the ellipse

Center of the ellipse $\to (0, 0)$

Since, $b > a$ ,

Ellipse will be vertical.

$a^{2} = 9 \Rightarrow a = \pm 3 b^{2} = 16 \Rightarrow b = \pm 4$

Therefore, endpoints of the axes are,

Endpoints of the horizontal axis $\to (- 3, 0), (3, 0)$

Endpoints of the vertical axisrole="math" localid="1645632245020" $\to (0, - 4), (0, 4)$

Step 3. Graph the equation

Graph of the equation will be,

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In the following exercises, graph each equation.
$16 x^{2} + 9 y^{2} = 144$

Short Answer

Step by step solution

Step 1. Standard form of the equation,

Step 2. Key features of the graph,

Step 3. Graph the equation

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In the following exercises, graph each equation.16x2+9y2=144

Short Answer

Step by step solution

Step 1. Standard form of the equation,

Step 2. Key features of the graph,

Step 3. Graph the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Pure Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation.
$16 x^{2} + 9 y^{2} = 144$