# Course Activity_ Equation of a Parabola Based on Its Focus and Directrix.pdf

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TaskDeriving the Equation of a Parabola Given aFocus and DirectrixIn this task, you will create a vertical parabola and a horizontal parabola based on the instructions provided.You will also practice writing equations of these parabolas.Question 1The vertex form of the equation of a vertical parabola is given by, where (h, k) is thevertex of the parabola and the absolute value ofpis the distance from the vertex to the focus, which is alsothe distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a verticalparabola and write the vertex form of its equation. OpenGeoGebra , and complete each step below. If youneed help, follow theseinstructions for using GeoGebra.Part AMark the focus of the parabola you are going to create atF(6, 4). Draw a horizontal line that is 6 units belowthe focus. This line will be the directrix of your parabola. What is the equation of the line?
Part BConstruct the line that is perpendicular to the directrix and passes through the focus. This line will be theaxis of symmetry of the parabola. What are the coordinates of the point of intersection,A, of the axis ofsymmetry and the directrix of the parabola?

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