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Algebra 2 Conic Sections

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1.     The equation of a hyperbola is given by

         y^2/25 - (x-6)^2 / 144 = 1

(a)   Identify the coordinates of the center of the hyperbola.

(b)   Find the length of the transverse and conjugate axes.

(c)   Find the slopes of the asymptotes.

(d)   Graph the hyperbola.

asked Jan 26, 2017 in ALGEBRA 2 by Doll_girl98 Novice
reshown Jan 26, 2017 by goushi

1 Answer

0 votes

Step 1:

The equation of hyperbola is image

a)

Find the center of the hyperbola.

Standard form of the hyperbola transverse axis is vertical

image

Compare between standard form of the hyperbola equation and equation of the hyperbola.

image

b)

Find the length of the transverse and conjugate axis.

Here, Vertices are

image

The transverse axis is image

The conjugate axis is image

Substitute image

image

The transverse and conjugate axis image

c)

Find the slopes of the asymptotes.

The equations of the asymptotes for a vertical transverse axis hyperbola is image

Substitute image

image

The slopes of the asymptotes image

d)

Graph the hyperbola.

Graph the hyperbola equation image

image

Solution:

image

b) The transverse and conjugate axis image

c) The slopes of the asymptotes image

d)

image

answered Jan 26, 2017 by Anney Mentor

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