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.
You might be interested in
Option B: is the area of the compact disc.
Explanation:
The diameter of the compact disc is .
To determine the area of the compact disc, let us substitute the values in the area of the circle formula,
where
Substituting the value of d in , we get,
Thus, and
. Let us substitute these values in
, we get,
Simplifying, we have,
Multiplying, we get,
Thus, the area of the compact disc is
Hence, Option B is the correct answer.
Assuming you know the quadratic formula:
You can fill in a, b and c in this and get:
Now, let's create a shorthand to make the writing easier:
But since one root is three times the other root (but we don't know which one), we also know that:
or
If you solve this, you get:
or
However, since q is a square root, it must be postive.
So we know that:
From this you find that
So p = 3/2
The roots are x=1/2 and x=3/2.