Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,960 users

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola.

0 votes
Find  the  center,  vertices,  foci,  and  the equations of the asymptotes of the hyperbola. Use a graphing utility to graph the hyperbola and its asymptotes.

9y^2 - x^2 + 2x + 54y + 62 = 0
asked Feb 2, 2015 in TRIGONOMETRY by anonymous
reshown Feb 2, 2015 by goushi

1 Answer

0 votes

Step 1:

The equation is .

Group the terms.

Complete each square.

Compare it to the standard form of the hyperbola .

Here transverse axis is parallel to the axis.

is the center of the hyperbola.

is the distance between center and focus.

.

Step 2:

The center of the hyperbola is .

The vertices of the hyperbola are .

The foci of the hyperbola are .

Find the points to form a rectangle.

.

.

The extensions of the diagonals of the rectangle are the asymptotes of the hyperbola.

Asymptotes of the hyperbola are .

Substitute the values of in .

Asymptotes are .

Step 3:

Graph :

(1) Draw the coordinate plane.

(2) Draw the equation of the hyperbola.

(3) Plot the foci and vertices.

(4) Form a rectangle containing the points , .

(5) Draw the asymptotes of the hyperbola.

image

Solution :

The equation of the hyperbola is .

The center of the hyperbola is .

The vertices of the hyperbola are .

The foci of the hyperbola are .

Asymptotes of the hyperbola are .

Graph of the hyperbola and asymptotes :

image

answered Feb 7, 2015 by joseph Apprentice

Related questions

...