Which term best describes the set of all points in a plane for which the sum
of the distances to two fixed points equals a certain constant?

elipse

step-by-step explanation:

in mathematics, an  ellipse  is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. as such, it is a generalization of a circle, which is a special type of an  ellipse having both focal points at the same location.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."