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Homework Statement
Find the equation of a parabola with a vertex of (1,-3) and focus of (1,-1)?
Find the equation of a parabola with a given focus and vertex.
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SUMMARY
The equation of a parabola with a vertex at (1, -3) and a focus at (1, -1) can be derived using the standard form of a vertical parabola. The distance from the vertex to the focus is 2 units, indicating that the directrix is located at (1, -5). The final equation of the parabola is (x - 1)² = 8(y + 3), where the value 8 is derived from the distance to the focus squared.
PREREQUISITES- Understanding of the standard form of a parabola equation
- Knowledge of vertex and focus coordinates
- Familiarity with the concept of directrix
- Basic algebra for manipulating equations
- Study the derivation of the standard form of a parabola equation
- Learn about the properties of parabolas, including directrix and focus
- Explore applications of parabolas in physics and engineering
- Practice solving problems involving parabolas with different orientations
Students studying algebra, geometry enthusiasts, and anyone looking to understand the properties and equations of parabolas.