Question

Find the center, vertices, foci, and the equations  of  the  asymptotes  of  the  hyperbola,  and  sketch  its graph using the asymptotes as an aid.

Answer 1

Step 1:

The hyperbola equation is .

The y - term is positive then the hyperbola is vertical.

The standard form of vertical hyperbola equation is .

Where is the center of the hyperbola, is the length of the semi transverse axis and is the semi conjugate axis.

Compare with standard form of vertical hyperbola.

The center of the hyperbola is , and .

Find length of the semi transverse axis.

Find the length of the semi conjugate axis.

Step 2:

The standard form of vertical hyperbola is .

Foci are   vertices are and asymptotes are .

The hyperbola equation is .

Foci are .

Vertices are .

The asymptotes are

 The asymptotes are .

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Step 3:

Plot the center point .

Plot the focus points and vertex points  .

Draw the asymptotes are .

Sketch the hyperbola.

Solution:

The center of the hyperbola .

The vertices are .

The foci are .

The asymptotes are .