Question

Find the coordinates of the center, vertices, covertices, foci, length of transverse and cojugate axis and the equation of the asymptotes. Then graph the parabola.

Answer 1

The given equation is:

`(x^2)/(9)-(y^2)/(49)=1`

The equation matches the general equation of a hyperbola given by:

`(x^2)/(a^2)-(y^2)/(b^2)=1`

Hence a=3 and b=7.

The center is at origin (0,0)

The vertices are at (3,0) and (-3,0)

The focii are:

`(\sqrt[]{58},0),(-\sqrt[]{58},0)`

The equation of the asymptotes are:

`y=(7x)/(3),y=-(7x)/(3)`

There are no covertices since the hyperbola does not have covertices.

The graph is given below: