Chapter 11: Q.181E (page 1135)

In the following exercises, graph each equation.
$y^{2} - x^{2} - 4 y + 2 x - 6 = 0$

Short Answer

Expert verified

Equation given in the question represents a hyperbola.

Step by step solution

Identification of the conic

Given equation of the conic is,

$y^{2} - x^{2} - 4 y + 2 x - 6 = 0$

Since, coefficients have the different signs, it's a hyperbola.

Convert the equation of the hyperbola in the standard form

$y^{2} - x^{2} + 2 x - 4 y - 6 = 0$

$(y^{2} - 4 y + 4) - (x^{2} - 2 x + 1) - 3 - 6 = 0$

${(y - 2)}^{2} - {(x - 1)}^{2} = 9$

$\frac{{(y - 2)}^{2}}{3^{2}} - \frac{{(x - 1)}^{2}}{3^{2}} = 1$

Transverse axis and center of the hyperbola

Since, $y^{2}$ term of the equation is positive, transverse axis will be vertical.

Center of the hyperbola $\to (1, 2)$

Graph of the hyperbola will be,

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

Draw a rectangle that passes through the points $3$ units above and below the center and $3$ units left and right to the center.

Sketch the asymptotes - lines through the diagonals of the rectangle.

Graph the branches and mark the vertices.

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.

In the following exercises, graph each equation.
$y^{2} - x^{2} - 4 y + 2 x - 6 = 0$

Short Answer

Step by step solution

Identification of the conic

Convert the equation of the hyperbola in the standard form

Transverse axis and center of the hyperbola

Graph of the hyperbola will be,

Graph the branches and mark the vertices.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Probability and Statistics

Discrete Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation.y2-x2-4y+2x-6=0

Short Answer

Step by step solution

Identification of the conic

Convert the equation of the hyperbola in the standard form

Transverse axis and center of the hyperbola

Graph of the hyperbola will be,

Graph the branches and mark the vertices.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Probability and Statistics

Discrete Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation.
$y^{2} - x^{2} - 4 y + 2 x - 6 = 0$