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.

x^2 - 9y^2 + 2x - 54y - 80 = 0

Answer 1

Step 1:

The conic equation is .

Convert the equation into standard form.

Change the expression and into a perfect square trinomials add (half the x coefficient)²  and (half the y coefficient)² to each side of the equation.

Compare with standard form of pair of intersecting lines .

The equation represents a pair of intersecting lines.

Step 2:

Find the intersecting point.

Comparing with .

Formula for the point of Intersection of the lines is .

Substitute the above values.

Graph:

Graph the equation :

Observe the graph the two lines are intesecting at .

Solution:

The equation represents a pair of lines and they are intersect at .