Which geometric object is defined as the set of all points in a plane equidistant from a single point and a single line?
2 answers:
Answer:
The geometric object that matches the definition is the parabola.
Step-by-step explanation:
A parabola is the set of all points in a plane equidistant from a fixed point (the focus) and a fixed-line (the directrix) that lie in the plane.
A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
An angle bisector is a line or ray that divides an angle into two congruent angles.
A hyperbola is the set of all points in a plane such that the absolute value of the difference of the distances between two fixed points stays constant.
Therefore the geometric object that matches the definition is the parabola.
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Answer:
The vertex is the point
Step-by-step explanation:
we have
we know ow that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
Convert the equation into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
therefore
the vertex is the point