A parabola has a vertex at $(0,0)$. The equation for the directrix of the parabola is $x=-4$.
In which direction does the parabola open?
up
down
right
left
Answer (2)
The vertex of the parabola is at ( 0 , 0 ) .
The directrix is the line x = − 4 .
Since the directrix is a vertical line to the left of the vertex, the parabola opens to the right.
The parabola opens to the right .
Explanation
Problem Analysis The problem states that a parabola has its vertex at ( 0 , 0 ) and its directrix is given by the equation x = − 4 . We need to determine the direction in which the parabola opens.
Determining the Direction The directrix of a parabola is a line such that every point on the parabola is equidistant from the directrix and the focus. Since the directrix is a vertical line x = − 4 , the parabola must open either to the left or to the right. The vertex of the parabola is located at ( 0 , 0 ) . The directrix, x = − 4 , is to the left of the vertex. Therefore, the parabola opens to the right.
Conclusion The parabola opens to the right.
Examples
Parabolas are commonly seen in the design of satellite dishes and reflecting telescopes. The parabolic shape helps to focus incoming signals or light to a single point, the focus. Understanding the direction a parabola opens is crucial in these applications to ensure the receiver or light sensor is placed correctly at the focus.
The parabola opens to the right, as its directrix is located to the left of the vertex. Therefore, the correct answer is ' right '.
;
