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:
C
Step-by-step explanation:
We can use the factored form of the quadratic equation, given by:
Where <em>a</em> is the leading coefficient and <em>p</em> and <em>q</em> are the zeros.
We have zeros <em>x</em> = -2 and <em>x</em> = 3. So, let <em>p</em> = -2 and <em>q</em> = 3:
Next, we are given that our <em>y-</em>intercept is (0, -30).
In other words, when <em>x</em> = 0, <em>y</em> = -30. So:
Solve for <em>a:</em>
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Hence, our factored equation is:
For the standard form, expand:
Simplify:
Distribute:
Our answer is C.