QuestionThe axis of symmetry of a parabola is always parallel to the directrix. True False
Studdy Solution
STEP 1
1. A parabola is defined as the set of all points equidistant from a point called the focus and a line called the directrix.
2. The axis of symmetry of a parabola is a line that passes through the focus and is perpendicular to the directrix.
STEP 2
1. Define the axis of symmetry and directrix of a parabola.
2. Analyze the relationship between the axis of symmetry and the directrix.
3. Determine the truth value of the statement.
STEP 3
Define the axis of symmetry and directrix of a parabola:
- The axis of symmetry is a line that divides the parabola into two mirror-image halves. It passes through the vertex and the focus of the parabola.
- The directrix is a line that is equidistant from the vertex as the focus is, but it lies on the opposite side of the vertex from the focus.
STEP 4
Analyze the relationship between the axis of symmetry and the directrix:
- The axis of symmetry is perpendicular to the directrix. This means they intersect at a right angle.
STEP 5
Determine the truth value of the statement:
- Since the axis of symmetry is perpendicular to the directrix, it is not parallel to the directrix.
The statement "The axis of symmetry of a parabola is always parallel to the directrix" is:
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