Algebra 2 Conic Sections

Question

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.

Answer 1

Step 1:

The equation of hyperbola is

a)

Find the center of the hyperbola.

Standard form of the hyperbola transverse axis is vertical

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

b)

Find the length of the transverse and conjugate axis.

Here, Vertices are

The transverse axis is

The conjugate axis is

Substitute

The transverse and conjugate axis

c)

Find the slopes of the asymptotes.

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

Substitute

The slopes of the asymptotes

d)

Graph the hyperbola.

Graph the hyperbola equation

Solution:

b) The transverse and conjugate axis

c) The slopes of the asymptotes

d)