Find the vertex, focus, and directrix of the parabola, and sketch its graph. (x – 3)² – 2(y + 5) = 0 vertex (x, y) -(| focus (х, у) - directrix y \15 10 10 5 10 -5 10 -10 5 10 10 -15 Find the standard form of the equation of the parabola with the given characteristics. focus: (3, 3) directrix: x --3 (y- 3)2 = 12x Find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph. 36x2 + y2 - 36 center: (x, y) = (

Q: Consider a horizontal parabola of the form ay² + by + c = x where a = 0, and whose graph contains…

A: We have to find the equation of horizontal parabola  ay2+by+c=x The graph contains the points -1,3.…

Q: Find the standard form of the equation of the parabola with the given characteristics. Vertex:…

A: General equation of parabola,(x-h)2 = 4p(y-k)where (h,k) is Vertexy = k-p is directrix

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A: Given equation of hyperbola is: x+3225-y-3216=1 To find the center, foci, ends of major axis, end of…

Q: Find the vertex, focus, and directrix of the parabola. y² + 2y + 16x + 33 = 0 (x, y) = vertex focus…

A: The given equation of parabola is:             y2+2y+16x+33=0⇒ y2+2y+1+16x+32=0⇒…

Q: 1. Consider the parabola with focus point (1, 1) and directrix the horizontal line y = -3. a) What…

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A: We have given some key point about parabola, we have to find, equation of parabola.

Q: 7) Determine the shape of the I point parabola with focus F(2,5/2) and directrix line y=7/2. *

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Q: Find the standard form of the equation of the parabola with the given characteristics. Directrix: y…

A: Standard form of equation of parabolla is given by :x-h2=4ay-kThe distance between 0,2&8,2 is…

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A: Parabola is a U-shaped curve and it is part of a conic section.  The focus of the parabola is the…

Q: 5) Find the vertex and axis of symmetry of the parabola with focus F(7/2,3) and directrix line…

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Q: 6. Find the equation of the parabola with vertex (-2, 5) and focus (-4, 5). (10 points)

A: Given the vertex (-2,5) and focus (-4,5) of a parabola To find the equation of the parabola It is…

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Q: Activity 2 Classify the graph of the equation as circle, a parabola, an ellipse, or a hyper Show…

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Q: Find an equation for the parabola with vertex V(0, 0) and Focus F(0, 2), and sketch its graph.

A: We have given vertex V0,0 and focus F0,2. Given the vertex of the parabola is V0,0 and focus is at…

Q: Determine the axis of symmetry of a parabola with directrix x = -6 and vertex at (7,4). Determine…

A: Let's find.

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A: Step:-1 For a hyperbola x2a2 -y2b2=1 ----(1)  with center at origin and opens left and right, we…

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Q: Find an equation of the parabola with vertex (3, 4) and directrix y = 1.

A: Graph of parabola :

Q: 4. Find the equation of the parabola with focus at (0, 6) and the directrix defined by the equation…

A: 5

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A: Solution of the problem as follows

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A: The given hyperbola has center at origin length of the vertical conjugate axis is 6 units of the…

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A: A detailed solution is given below.

Q: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

Q: Consider a horizontal parabola of the form ay² +by+c = x where a 0, and whose graph contains the…

A: Given: A horizontal parabola ay2+by+c=x, where a≠0 and whose graph contains the points -1, 3, 2, 4…

Q: 21. What's the standard form equation of a parabola with directrix x = -10 and focus (10,0)?

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Q: Find the vertex, focus, and directrix of the parabola, and sketch its graph. v= -12x vertex (x, y) -…

A: we have to find the following

Q: 9) Write the standard form of the equation of the hyperbola with vertices (0,2), (6,2) and…

A: Vertices (h-a,k),(h+a,k) asymptotes y=+-(b/a)(x-h)+k

Q: What are the equations of the asymptotes of the hyperbola? (z+1)* _ y-3}° (v-3)? 16 25 Enter your…

A: The equation of the given Hyperbola is: (x+1)225-(y-3)216=1

Q: Find an equation of the parabola with vertex (4, 2) and directrix y=−1

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Q: Consider a horizontal parabola of the form ay² + by + c = x where a 0, and whose graph contains the…

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Q: (Part II) Graph the parabola from Part 1. 22 --20y %3D

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Q: equation of the parabola whose focus is located at (9,8) and the equation of directrix is x= -2 ect…

A: let P(x, y) be the point on the parabola having the focus S = (9, 8) and the directrix is x = -25…

Q: Vertices at (0,1) and (0, -1); asymptotes are the lines x = +3y

A: It is given that the vertices of the hyperbola are (0,1) and (0,-1) and the asymptotes are x=±3y.…

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Q: A parabola has a focus located at (5, -) and a directrix of y = What are the coordinates for the…

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Q: What is the equation of the parabola whose focus is at the origin ?(0,0) and whose directrix passes…

A: To sketch the parabola whose focus is the origin and directrix passes through the points (−4,0) and…

Q: Describe the graph of the equation. r = 8sin 14ti – 8cos 14tj O It is a parabola in the xy-plane,…

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Q: A hyperbola is defined by the equation x2 - y2 - 2x - 4y - 4 = 0. Its center is at the point (-1, 2)…

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Q: a) Detemine the equation of the hyperbola having the equations of asymptote y = 3D7x, conjugate axis…

A: Consider the given: The standard form of the equation of a hyperbola with center 0,0 andtransverse…

Q: 7) Determine the shape of the parabola with focus F(7/2,3) and directrix line x=1/2. *

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Q: 3. %3D Find an equation of the hyperbola that has foci at (0, - 15) and (0, 15), and asymptotes y=…

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Q: Find an equation of the parabola with focus (-1,-4) and directrix x=1

A: We can find the equation of parabola as below.

Q: 7) Find the standard form of the equation for the parabola with vertex (1,2) and directrix y -1.

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Q: Determine the standard form of equation of a parabola give its parts and properties. 1. Vertex at…

A: Given that: 1. Vertex is at origin and DL at x=52. F(3,3) and V(3, 6)3. F(-2, 6) and DL at y=-2