Question

find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola 9.2x = y² focus = directrix = focal diameter = vertex = axis of symmetry = be sure to enter each answer in the appropriate format. hint: what is the appropriate notation for a line or a point? question help: video

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a parabola of the form \(y^{2}=4px\). Given \(9.2x = y^{2}\), we can rewrite it as \(y^{2}=9.2x\). Comparing with \(y^{2}=4px\), we have \(4p = 9.2\), so \(p=\frac{9.2}{4}=2.3\)

Step2: Find the focus

For a parabola \(y^{2}=4px\), the focus is \((p,0)\). Since \(p = 2.3\), the focus is \((2.3,0)\)

Step3: Find the directrix

The directrix of the parabola \(y^{2}=4px\) is \(x=-p\). Since \(p = 2.3\), the directrix is \(x=- 2.3\)

Step4: Find the focal diameter

The focal diameter of the parabola \(y^{2}=4px\) is \(|4p|\). Since \(4p=9.2\), the focal diameter is \(9.2\)

Step5: Find the vertex

The vertex of the parabola \(y^{2}=4px\) is \((0,0)\)

Step6: Find the axis of symmetry

For the parabola \(y^{2}=4px\), the axis of symmetry is the \(x -\)axis, whose equation is \(y = 0\)

Answer:

Focus = \((2.3,0)\)
Directrix = \(x=-2.3\)
Focal diameter = \(9.2\)
Vertex = \((0,0)\)
Axis of symmetry = \(y = 0\)