Final answer:
The equation y = 7/x represents a hyperbola, not an ellipse, circle, or parabola. This is because it has a reciprocal relationship between y and x, which is characteristic of hyperbolas.
Step-by-step explanation:
The equation given in the question, y=(7)/(x), represents a hyperbola, not an ellipse, circle, or parabola. In general, the equation of a hyperbola in Cartesian coordinates has a form that involves a term with x in the denominator, such as y=k/x where k is a constant.
This is because a hyperbola is one of the conic sections, which also include ellipse, circle, and parabola. These conic sections are the result of the intersection of a plane with a cone, as shown in Figure 3.3 Conic Sections.
The provided equation is a specific case of conic sections where the coefficients that would define a parabola or ellipse are not present, hence, it does not represent a parabolic or elliptic curve.
Instead, it represents a hyperbola because it is the graph of an equation with an inverse variation between x and y. In contrast, a circle is a special case of an ellipse where the two foci are at the same point, and a parabola has a general form y=ax+bx² with specific coefficients.