1. Determine the focus and directrix of the parabola with the given equation. Sketch the graph, and indicate the focus, directrix, and vertex. a. y? = 20x b. 3x2 = -12y c. x2-6x-2y +9 = 0 d. 3y2 + 8x + 24y + 40 = 0 %3D 2. An object thrown from a height of 2 m above the ground follows a parabolic path until the object falls to the ground (see figure below). If the object reaches a maximum height (measured from the ground) of 7 m after travelling a horizontal distance of 4 m, determine the horizontal distance between the object's initial and final positions. 7 m m

Q: What is the standard form of the equation of the parabola with the focus (5, –1) and the directrix æ…

A: Any point at parabola is equidistant from its focus and directrix.

Q: Find the focus and directrix of the parabola given by y2 = 8x.Then graph the parabola.

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Q: Determine an equation for the parabola with focus (3,2) and directrix y = -4.

A: Since, directrix is vertical use equation of parabola that opens up or down.     (x-h)2 = 4p(y-k)…

Q: Find the standard form of the equation of a parabola with focus (5,0) and directrix x = -5,shown in…

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Q: The focus of a parabola is (-3,5) and the directrix is y = -1. Which equation represents a parabola…

A: Given the focus of parabola is -3,5 and directrix is y=-1.

Q: Given a parabola's focus at (6, −4) and directrix at y = −7, how would you write its equation?

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

Q: Determine the equation of a parabola with focus at (0,5) and directrix y=5

A: Given, The parabola with focus at 0, 5  and directrix is y=5 We have to find the equation of the…

Q: 31. Find the coordinates of the focus of the parabola whose equation is x² – 18x + 24y + 273 = 0. С.…

A: Since you have asked multiple unrelated questions in a single request, we would be answering only…

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus: (0,…

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Q: 3- If the equation of the hyperbola is 4x? – 9y? = 36 Find the distance between the negative foci…

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Q: Consider the parabola whose vertex us at (2,-1) amd focus at (0,-1). What is the general form of the…

A: Given, The vertex of the parabola = 2, -1  Focus of the parabola = 0,-1 We have to write the general…

Q: Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)? Focus…

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Q: Find the focus and directrix of the parabola given by y2 = 12x. Then graph the parabola.

A: y2=12x Now comparing with y2=4ax, we get 4a=12⇒a=3 Therefore focus is, a, 0=3, 0 & directrix is,…

Q: 17. If the focus of the parabola is (-2, 1) and the directrix has the equation x + y = 3 then the…

A: Given Focus of parabola f (-2, 1) Equation of directrix is x+y =3   Here the objective is to find…

Q: Find the equation for the parabola that has its vertex at the origin and the focal point is 278…

A: Consider the equation of parabola vertex at origin and focus to the right of directrix. y2=4ax…

Q: Find the Parabola with Focus (7,-2) and Directrix x=-9

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Q: An engineer is designing a flash light using a parabolic reflecting mirror and a light source, shown…

A: Provided figure is Diameter=2x=4 ⇒ x=2 Depth=y=2

Q: Consider the hyperbola with equation x2 /A2 − y2 /B2 = 1. Let F be the focus with coordinates (√A2 +…

A: Given The hyperbola equation is x2A2-y2B2=1, the focus with coordinates A2+B2, 0 . e=A2+B2A and the…

Q: Find the equation of the parabola with focus (8,0) and directrix x -8

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

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Q: Can you assist me in answering this? (Not graded - solely for acquisitional purposes)

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: given, focus (0,15) directrix y=-15

Q: Solve the following problems. 1. Determine the focus and directrix of the parabola with the given…

A: As per our guidelines we are supposed to solve only first 3 problems. Please re-post the other…

Q: What is the equation of a parabola in vertex form with focus (9, 5) and directrix y = 3? A. y =…

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Q: 3+ 2 Focus: (0, 2) 1+ -1 o -1+ Directrix: y--2 -3+

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Q: find the equation of the parabola with the given  Focus (2, 0), directrix x = −2

A: Our Aim is to find the equation of the parabola with the given Focus (2,0) and directrix x=-2.

Q: Consider the following equation of a parabola. (y - 6) = 4(x - 6) %3D Step 1 of 3: Find the focus of…

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Q: 24. Construct the equation of a parabola with focus at (-1,2) and a directrix x = -7.

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Q: 4. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola and then…

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Q: 2. Write the equation of the parabola x+ 6x+8y = 7 in standard form and identify the a) vertex, b)…

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Q: Determine the equation of the parabola given the focus at (-10,23/2) and directrix at y=-11/2.…

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Q: Write the equation of the parabola with focus at (3,5) and directrix y = 3.

A: First I have written a formula of parabola with given focus and directrix, just use the formula for…

Q: 1. Marsha was completing the steps for a parabola that has a focus at (5,-2) with directrix at y =…

A: Formula:-1)Distance between two points (x1,y1) & x2,y2 is d=(x1-x2)2+(y1-y2)22)Distance of a…

Q: Consider the hyperbola of equation: (y – k)2 (x - h)2 1 a? 62 whose foci are (3, -1) and (3, 17),…

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Q: 3+ 2 Focus: (0, 2) 1+ -3 -2 -1 o -1+ -2- Directrix: y= -2 -3+

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Q: given the directrix of y = 6 and focus of (0, 4) which is the equation of the parabola

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Q: 19. State whether the graph of the equation below is an ellipse, circle, parabola, or hyperbola. 2x…

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Q: Find an equation of the parabola with focus (4, 4) and directrix x=0.

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: Given : Direction : y = 25 Focus : ( 0 , -25 ) Vertex is exactly between Directrix and Focus

Q: given the directrix of y = 6 and focus of (0,40, which is the equation of the parabola?

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Q: Which are the foci for the hyperbola modeled by the equation (Y-32 (x-1)² _ -1? 36 13

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Q: Picture of question is attached.

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Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (1,…

A: Given: A rough sketch of the parabola shall be as follows:

Q: 7. Find the focus, directrix and focal diameter of the parabola 3y =-24x, and sketch its graph.

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Q: Find the focus, directrix, and focal diameter of the parabola y = x², and sketch its graph.

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus: (12,…

A: Alternatively, you can use the definition of a parabola to derive the equation. A parabola is the…

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (2,…

A: Consider trhe focus of the parabola is 2,4 and the directrix is x=-4. Let x,y be any point on the…

Q: Determine the equation and sketch the graph the parabola given focus at (12, 3) and directrix at x =…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.