Which of the following terms best describes the set of all points in a plane for which the difference between the distances of a given point to two fixed foci equals a certain constant?

HYPERBOLA

Step-by-step explanation:

We have the statement,

'The set of all points in a plane for which the difference between the distances of a given point to two fixed foci equals a certain constant'.

We know that,

Hyperbola is the set of points such that for point P anywhere on the curve, the absolute distance to the two fixed points is a constant.

i.e. From the figure, we see that, the difference of the distance of P from and is equal to constant 2a.

Thus, the term representing the given statement is HYPERBOLA.

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3