Problem

Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola
43.6x=y2

Focus
Directrix
Focal diameter =
Vertex
Axis of symmetry

Answer

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Answer

Final Answer: The focus of the parabola is at (10.9,0), the directrix is x=10.9, the focal diameter is 43.6, the vertex is at the origin (0,0), and the axis of symmetry is the y-axis x=0.

Steps

Step 1 :The given equation is in the form of y2=4ax, where 4a=43.6.

Step 2 :Calculate the value of a, a=43.64=10.9.

Step 3 :The focus of the parabola is at (a,0), so the focus is at (10.9,0).

Step 4 :The directrix of the parabola is x=a, so the directrix is x=10.9.

Step 5 :The focal diameter of the parabola is 4a, so the focal diameter is 43.6.

Step 6 :The vertex of the parabola is at the origin (0,0).

Step 7 :The axis of symmetry of the parabola is the y-axis x=0.

Step 8 :Final Answer: The focus of the parabola is at (10.9,0), the directrix is x=10.9, the focal diameter is 43.6, the vertex is at the origin (0,0), and the axis of symmetry is the y-axis x=0.

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