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

Question

Find the <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Center,foci, and vertices of the hyperbola, and sketch its graph using asymptotes as an aid.

Answer 1

Step 1:

The hyperbola equation is .

Convert the equation into standard form of hyperbola.

To change the expressions  and  into a perfect square trinomial,

add (half the x coefficient)² and add (half the y coefficient)² to each side of the equation.

Compare with standard form of vertical hyperbola is .

Where  is the center of the hyperbola.

Foci are , vertices are and asymptotes are .

Step 2:

The center of the hyperbola is , and .

Foci are .

Vertices are .

Vertices are .

The asymptotes are .

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Step 3:

Graph the hyperbola.

Graph the equation .

Plot the center point .

Plot the focus points .

Plot the vertex points  .

Draw the asymptotes are .

Solution:

Foci are .

Vertices are .

The asymptotes are .