Chapter 9: Q. 58 (page 773)

Prove Theorem 9.20 (b). That is, show that the graph of the equation satisfies $\frac{y^{2}}{B^{2}} - \frac{x^{2}}{A^{2}} = 1$ Definition 9.19, where the points with coordinates $(0, \pm \sqrt{A^{2} + B^{2}})$ are the foci of the hyperbola

Short Answer

Expert verified

Hence, proved

Step by step solution

Given information

The given equation of a parabola is $\frac{y^{2}}{B^{2}} - \frac{x^{2}}{A^{2}} = 1$

Stp 2: Graph the parabola and find the vertices and foci.

The graph of the parabola $\frac{y^{2}}{B^{2}} - \frac{x^{2}}{A^{2}} = 1$ is ,

The coordinates of the hyperbola are $(0, \pm \sqrt{A^{2} + B^{2}})$

As, from the graph it is clear that the points with coordinates $(0, \pm \sqrt{A^{2} + B^{2}})$

are the foci of the hyperbola.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Prove Theorem 9.20 (b). That is, show that the graph of the equation satisfies $\frac{y^{2}}{B^{2}} - \frac{x^{2}}{A^{2}} = 1$ Definition 9.19, where the points with coordinates $(0, \pm \sqrt{A^{2} + B^{2}})$ are the foci of the hyperbola

Short Answer

Step by step solution

Given information

Stp 2: Graph the parabola and find the vertices and foci.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Discrete Mathematics

Probability and Statistics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Prove Theorem 9.20 (b). That is, show that the graph of the equation satisfiesy2B2-x2A2=1 Definition 9.19, where the points with coordinates 0,±A2+B2 are the foci of the hyperbola

Short Answer

Step by step solution

Given information

Stp 2: Graph the parabola and find the vertices and foci.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Discrete Mathematics

Probability and Statistics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Prove Theorem 9.20 (b). That is, show that the graph of the equation satisfies $\frac{y^{2}}{B^{2}} - \frac{x^{2}}{A^{2}} = 1$ Definition 9.19, where the points with coordinates $(0, \pm \sqrt{A^{2} + B^{2}})$ are the foci of the hyperbola