Question

find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola:
14.28y = x²
the focus is
the directrix is
the focal diameter is
the vertex is
the axis of symmetry is
be sure to enter each answer in the appropriate format. hint: what is the appropriate notation for a line or a point?
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Explanation:

Step1: Rewrite in standard form

The given equation is $14.28y = x^2$. Rewrite as $y = \frac{1}{14.28}x^2$. Compare with the standard form $y = \frac{1}{4p}x^2$, so $4p = 14.28$.

Step2: Calculate p

Solve for $p$: $p = \frac{14.28}{4} = 3.57$.

Step3: Find focus

Focus of $x^2 = 4py$ is $(0, p)$, so $(0, 3.57)$.

Step4: Find directrix

Directrix is $y = -p$, so $y = -3.57$.

Step5: Find focal diameter

Focal diameter is $4p = 14.28$.

Step6: Find vertex

Vertex of $x^2 = 4py$ is $(0, 0)$.

Step7: Find axis of symmetry

Axis of symmetry is the y-axis ($x = 0$).

Answer:

Focus: $(0, 3.57)$
Directrix: $y = -3.57$
Focal diameter: $14.28$
Vertex: $(0, 0)$
Axis of symmetry: $x = 0$