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Chapter 11: Q. 336 (page 1160)

a) Identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and b) Graph the equation.

y2100-x236=1

Short Answer

Expert verified

The graph of equation is hyperbola.

Step by step solution

01

Step 1. Given Information

Given that the equation isy2100-x236=1.

02

Step 2. Standard form of hyperbola

The standard form of hyperbola can be denoted as,

(x-h)2a2-(y-k)2b2=1(Horizontalhyperbola)(y-k)2a2-(x-h)2b2=1(Verticalhyperbola)

It show that the standard form of vertical hyperbola and the graph is hyperbola.

03

Step 3. Conversion of standard graph

On converting the standard form,

(y-0)2102-(x-0)262=1

The hyperbola equation has positive y2term. The hyperbola centered at point (0,0). The vertices are (0,10) and (0,-10).

04

Step 4. Graph of the equation

On drawing the graph of the equation,

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