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 that opens to the left or right is \((y - k)^2=4p(x - h)\). Given \(-9.2x=y^{2}\), we can rewrite it as \(y^{2}=-9.2x\). Here \(h = 0,k = 0\), and \(4p=-9.2\), so \(p=\frac{-9.2}{4}=-2.3\)

Step2: Find the focus

For a parabola of the form \((y - k)^2 = 4p(x - h)\), the focus is \((h + p,k)\). Substituting \(h = 0,k = 0,p=-2.3\), the focus is \((-2.3,0)\)

Step3: Find the directrix

The directrix of a parabola of the form \((y - k)^2=4p(x - h)\) is \(x=h - p\). Substituting \(h = 0,p=-2.3\), we get \(x=0-(-2.3)=2.3\)

Step4: Find the focal diameter

The focal diameter is \(|4p|\). Since \(4p=-9.2\), the focal diameter is \(| - 9.2|=9.2\)

Step5: Find the vertex

For a parabola of the form \((y - k)^2=4p(x - h)\), the vertex is \((h,k)\). Here \(h = 0,k = 0\), so the vertex is \((0,0)\)

Step6: Find the axis of symmetry

For a parabola of the form \((y - k)^2=4p(x - h)\), the axis of symmetry is \(y = k\). Here \(k = 0\), so the axis of symmetry is \(y = 0\)

Answer:

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