Question

Identify this conic section.

x2 - y2 = 16
o line
circle
ellipse
parabola
hyperbola

Answer 1

hyperbola

Explanation:

hyperbola

Ax^2+By^2+Cx+Dy+E=0

A=B you probably have a circle

A and B have same sign but A isn't B you probably have an ellipse

A and B are opposite in sign you probably have an hyperbola

If either A or B=0 (but not both) then you have a parabola

Answer 2

Hyperbola

EXPLANATION

The given conic has equation:

`{x}^(2) - {y}^(2) = 16`

We divide through by 16.

`\frac{ {x}^(2) }{16} - \frac{ {y}^(2) }{16} = (16)/(16)`

We simplify the right hand side to get

`\frac{ {x}^(2) }{16} - \frac{ {y}^(2) }{16} = 1`

Or

`\frac{ {x}^(2) }{ {4}^(2) } - \frac{ {y}^(2) }{ {4}^(2) } = 1`

This is a hyperbola, that has its vertex at the origin because the quadratic terms have different signs. One is positive and the other is negative.