Concept explainers
Draw a graph of the parabola using given data.
Answer to Problem 1PS
The equations of the parabola are
Explanation of Solution
Given:
The distance between the focus and the directrix is the
Calculation:
A parabola is the set of all points in the plane equidistant from a given point (focus) and a given line (directrix).
The vertex, exactly between the focus and directrix.
Consider a parabola with focus
Let
Squaring both sides.
Similarly for negative
and for positive
In the given problem,
The vertex, exactly between the focus and directrix.
The distance between vertex to directrix
Now,
Directrixis
Equation of the parabolas are
Write the equation in the standard form of
Direction
Vertex
Focus
Directrix,
Draw a table for the
Hence the graph of the equation is given below.
Write the equation in the standard form of
Direction
Vertex
Focus
Directrix,
Draw a table for the
Hence the graph of the equation is given below.
Want to see more full solutions like this?
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning