Question

which statements describe a parabola? check all that apply. a parabola is the set of all points equidistant from the directrix and focus. the fixed line is called the vertex of a parabola. the focus is a fixed point inside the parabola. the line of symmetry intersects the focus and directrix. the line of symmetry and the directrix are perpendicular. the parabola intersects the directrix.

Explanation:

1. Statement 1: By definition, a parabola is the set of all points in a plane equidistant from a fixed point (focus) and a fixed line (directrix). So this is correct.
2. Statement 2: The fixed line is the directrix, and the vertex is the midpoint between the focus and the directrix (on the line of symmetry). So this is incorrect.
3. Statement 3: The focus is a fixed point inside the parabola (since the parabola opens towards the focus, and the directrix is outside relative to the focus's position). This is correct.
4. Statement 4: The line of symmetry (axis of symmetry) passes through the focus and is perpendicular to the directrix, so it intersects the directrix (at the point opposite the focus relative to the vertex). This is correct.
5. Statement 5: The line of symmetry is perpendicular to the directrix (as the directrix is a horizontal/vertical line and the axis of symmetry is vertical/horizontal in standard cases, or follows the perpendicular relationship in general). This is correct.
6. Statement 6: A parabola does not intersect the directrix (all points on the parabola are equidistant to focus and directrix, and the directrix is outside the parabola's "opening"). So this is incorrect.

Answer:

A. A parabola is the set of all points equidistant from the directrix and focus.
C. The focus is a fixed point inside the parabola.
D. The line of symmetry intersects the focus and directrix.
E. The line of symmetry and the directrix are perpendicular.