In Problems 39-56, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility. ( x − 3 ) 2 = − ( y + 1 )
In Problems 39-56, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility. ( x − 3 ) 2 = − ( y + 1 )
Solution Summary: The author explains the formula used to find the vertex, focus, and directrix of the parabola.
In Problems 39-56, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
Expert Solution
To determine
(a & b)
To find: Vertex, focus and directrix of the parabola given by, .
Answer to Problem 43AYU
Vertex: .
Focus: .
Directrix D: .
Explanation of Solution
Given:
Formula used:
Equation
Vertex
Focus
Directrix
Description
Parabola, axis of symmetry is parallel to , opens down.
Calculation:
The equation is of the form .
Hence, .
Therefore, vertex: .
Focus: .
Directrix D: .
Parabola, axis of symmetry is parallel to , and it opens down.
Expert Solution
To determine
c.
To graph: The parabola for the equation by hand and verify using a graphing tool.
Answer to Problem 43AYU
Explanation of Solution
Given:
.
Calculation:
The graph of the parabola .
By using the table above, we obtain few points and . We plot the graph of using these points and the graph opens down. The points are shown above in the graph.
Using graphing utility we verify the graph.
The Vertex , focus is shown in the graph above. The directrix D: is shown in the dotted line.
University Calculus: Early Transcendentals (3rd Edition)
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY