Title: Parabola at (h,k)
Course: 2025 Probabilidad y Estadística

Q: Find the vertex, focus, and directrix of the parabola, and sketch the graph.

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[Image]
- [Image] (Incorrect)
- [Image] (Correct)
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Incorrect)
A: [Image]

Q: Find the vertex and directrix of the parabola.

(y + 8) ^2 = -32x + 32
- vertex (1, -8), directrix x = 9 (Correct)
- vertex (8, -1), directrix x = -9 (Incorrect)
- vertex (1, 1), directrix y = -32 (Incorrect)
- vertex (-1, 8), directrix y = 16 (Incorrect)
- vertex (1, -8), directrix x = -9 (Incorrect)
A: vertex (1, -8), directrix x = 9

Q: Find the vertex and focus of the parabola.

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-5(x + 8) ^2 = y
- vertex (-5, 0), focus [Image] (Incorrect)
- vertex (0, -8), focus (-8, -5) (Incorrect)
- vertex (0, -8), focus [Image] (Incorrect)
- vertex (8, 0), focus (-8, -20) (Incorrect)
- vertex (-8, 0), focus [Image] (Correct)
A: vertex (-8, 0), focus [Image]

Q: Find the vertex, focus, and directrix of the parabola, and sketch the graph.

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[Image]
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Correct)
- [Image] (Incorrect)
- [Image] (Incorrect)
A: [Image]

Q: Find an equation for the conic whose graph is shown.

[Image]
- y^2 = 4.8(x- 2) (Incorrect)
- x^2 = 4.8(y- 2) (Incorrect)
- y^2 = 8(x + 1.2)^2 (Incorrect)
- y^2 = 4.8(x + 2) (Correct)
- y = 4.8(x + 2)^2 (Incorrect)
A: y^2 = 4.8(x + 2)

Q: Determine the length of the Latus Rectum of the parabola whose equation is \( y^2-28x-16y+8=0 \).
A: 28

Q: Determine the value of p of the parabola whose equation is \( y^2-28x-16y+8=0 \).
A: 7

Q: Determine the equation of the axis of the parabola whose equation is \( y^2-28x-16y+8=0 \).
A: y=8

Q: Determine the coordinates of the endpoints of the Latus Rectum of the parabola whose equation is \( y^2-28x-16y+8=0 \).. Input them as coordinates, separate by a comma like in the example. Do not write down L and R in the answer. No spaces between them.

Example: (3,8),(3,20)
A: (5,22),(5,-6) / (5,-6),(5,22)

Q: The parabola whose equation is \( x^2-8x+9y-17=0 \) is:
- Horizontal
- Vertical
- Oblique
- It is not possible to know with just the equation
A: Vertical