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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There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.
Answer:
Radius = OB= 27 cm
Apothem = 13.5 cm
A diagram is attached for reference.
Step-by-step explanation:
Given,
The perimeter of equilateral triangle ABC is 81/√3 centimeters.
Substituting this in the formula of perimeter of equilateral triangle =
Thus from the diagram , Side
We know each angle of an equilateral triangle is 60°.
From the diagram, OB is an angle bisector.
Thus °
Apothem is the line segment from the mid point of any side to the center the equilateral triangle.
Therefore considering ΔOBE, and applying tan function.
Thus ,apothem OE= 13.5 cm
Now for radius,
We consider ΔOBE
Thus for
Perimeter of equilateral triangle ABC is 81/√3 centimeters,
The radius of equilateral triangle ABC is 27 cm
The apothem of equilateral triangle ABC is 13.5 cm
