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Questions and Answers
What is the formula for a parabola?
What is the formula for a parabola?
- x² + y² = r²
- (x-h)² = 4p(y-k) (correct)
- y = mx + b
- (y-k)² = 4p(x-h)
What is the vertex of a parabola in coordinate form?
What is the vertex of a parabola in coordinate form?
(h, k)
What are the coordinates of the focus of a parabola?
What are the coordinates of the focus of a parabola?
(h, k+p)
What is the equation of the directrix of a parabola?
What is the equation of the directrix of a parabola?
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What is the axis of symmetry of a parabola?
What is the axis of symmetry of a parabola?
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The focus and the axis of symmetry of a parabola have different y-values.
The focus and the axis of symmetry of a parabola have different y-values.
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On a parabola, the focus and directrix are at equal distances from the points on the graph.
On a parabola, the focus and directrix are at equal distances from the points on the graph.
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Study Notes
Parabola Components
- Formula for a Parabola: Represents the standard form, given by ((x-h)² = 4p(y-k)), where (p) indicates the distance from the vertex to the focus.
- Vertex: The point where the parabola changes direction, represented by the coordinates ((h, k)).
Focus and Directrix
- Focus: A specific point inside the parabola, denoted as ((h, k+p)), which affects the shape and orientation of the curve.
- Directrix: A straight line given by (y = k-p) that is used to define the parabola alongside the focus.
Symmetry and Relationships
- Axis of Symmetry: The vertical line that passes through the vertex, represented by (x = h), indicating the line of symmetry in the parabola.
- Focus and Axis of Symmetry Relationship: The focus lies directly along the axis of symmetry, maintaining the same (y)-coordinate as the vertex.
- Focus and Directrix Distance: Any point on the parabola is equidistant from both the focus and the directrix, emphasizing the definition of a parabola.
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