Equation of a Parabola Based on Its Focus and Directrix_CA (2) (1).pdf

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Course ActivityEquation of a Parabola Based on Its Focus andDirectrixThe Lesson Activities will help you meet these educational goals:Content Knowledge—You will derive the equation of a parabola given a focusand directrix.Mathematical Practices—You will make sense of problems and solve them.DirectionsPleasesave this documentbefore you begin working on the assignment. Type youranswers directly in the document._________________________________________________________________________Teacher-Graded ActivitiesWrite a response for each of the following activities. Check the Evaluation section at theend of this document to make sure you have met the expected criteria for theassignment. When you have finished, submit your work to your teacher.Deriving the Equation of a Parabola Given a Focus and DirectrixThe vertex form of the equation of a verticalpara HYPERLINK""b HYPERLINK""olais given by, where(h,k) is the vertex of the parabola and the absolute value ofpis the distancefrom the vertex to the focus, which is also the distance from the vertex to thedirectrix. You will use the GeoGebra geometry tool to create a vertical parabolaand write the vertex form of its equation. OpenGeoGebra, and complete eachstep below. If you need help, follow theseinstructionsfor using GeoGebra.Mark the focus of the parabola you are going to create atF(6, 4). Draw ahorizontal line that is 6 units below the focus. This line will be the directrix ofyour parabola. What is the equation of the line?Type your response here: Y = Ax^2Construct the line that is perpendicular to the directrix and passes through thefocus. This line will be the axis of symmetry of the parabola. What are thecoordinates of the point of intersection,A,of the axis of symmetry and thedirectrix of the parabola?

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Term
Fall
Professor
NoProfessor
Tags
Conic section

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