How to describe the conic?

The first one is a hyperbola. You can tell because both x and y are squared and the sign of the coefficients are opposite.

It's centered on the origin and it has transverse axes of y = +/- x

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

The 2nd one is an ellipse

It is centered on the origin

It has a semi-major axis of 5 units that is parallel to the y-axis

It has a semi-minor axis of 2 units that is parallel to the x-axis

Conic section: circle, ellipse, parabola, hyperbola

1.the first one is a hyperbola (since its negative)

* x^2-y^2=9

= x^2/9- y^2/9=1 ( divide both side by 9 to make sure the equation is equal to 1)

2. the second one is an ellipse( since it is positive, if its negative than its hyperbola)

* 25x^2+ 4y^2=100

=x^2/4+ y^2/25=1 (divide both side by 100 and make sure its equal to 1)

so the final equation of the ellipse is x^2/4+ y^2/25=1

for more information go to: http://math2.org/math/algebra/conics.htm