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?
1 answer:
Answer:
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.
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Answer:
Surface area =
Volume =
Step-by-step explanation:
To find the surface area of our cone, we are using the formula for the surface area of a cone:
where
is the surface area
is the radius
is the height
Notice that the height, radius, and slant height make a right triangle, so to find the height, , we can use the Pythagorean theorem:
cm
We have all we need now to find the surface area of our cone:
Now, to find the volume of our cone, we are using the formula for the volume of a cone:
where
is the volume
is the radius
is the height
Replacing values
We can conclude that the surface area of our cone is 261.6 square centimeters and its volume is 281.2 cubic centimeters.