Exercises 1–4 give equations of parabolas. Find each parabola’s focus and directrix. Then sketch the parabola. Include the focus and directrix in your sketch. 1. y2 = -2x 2. x = -3y2 3. y = 4x2 4. x = 2y2

Q: Which is the equation of a parabola with focus (0, 5) and directrix y= -5?

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Q: Give the standard equation of the parabola with focus (-3,0) and directrix x=3

A: Standard equation of parabola is y2=±4ax Given that focus of parabola is (-3,0) and directrix is…

Q: Write the equation for the hyperbola with foci (-12, 6), (6, 6) and vertices (–10, 6), (4, 6). =1…

A: The hyperbola with foci (-12,6), (6,6) and vertices (-10,6), (4,6)

Q: What is the standard form equation of the hyperbola that has vertices (0, +4) and foci (0, +2/1…

A: Here we have vertices of the hyperbola (0,±4) and foci 0,±213

Q: Write the equation of a parabola in standard form from the following information: Focus (-5, 7)…

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Q: Write the equation for the hyperbola with foci (–12, 6), (6, 6) and vertices (-10, 6), (4, 6). =1…

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Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices:…

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Q: Write the standard form equation for each parabola described A. Vertex (5,-2),directrix =11/2 B.…

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Q: One point on a parabola is (–7, 17). The focus of the parabola is (5, 1). Which equation represents…

A: Given

Q: Write the equation of a parabola whose directrix is æ 0.25 and has a focus at (1.75, 6)

A: Given, The parabola whose  Directrix is x = 0.25 Focus at 1.75, 6  We have the write the equation…

Q: Find the equation of the parabola with a vertex at (2,1)  and focus at (2,3). Explain how to graph…

A: Topic:- parabola

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

A: Given problem is :

Q: Find the equation of the hyperbola with vertices (2, 5) and (2, –3) and foci (2, 10) and (2, –8).…

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Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (2,…

A: Given that the directrix is x = -2, we can conclude that the parabola opens to the right(in a…

Q: Find the standard form of the equation of the parabola with the given characteristics. Vertex: (6,…

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Q: EXERCISES 2.2 Write the equation of the parabola in standard from with vertex at the origin that…

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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: Write the Equation of the parabola: Focus: (0, -5), Directrix: y= -3

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Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: We use the general equation of left opening parabola y2=-4Ax and solve it.

Q: Write an equation of a parabola with a vertex at the origin and a focus at (4, 0)

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Q: What is the equation of a parabola with directrix x 3/2 and focus (5/2, 4)? Oy- 5=- Oz-5 = - Oy-5 =…

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Q: find the equation of the parabola with the given properties. Vertex (0, 0), directrix y = −5

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Q: Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and…

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

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Q: Use the information provided to write the standard form equation of the hyperbola. Vertices: (8, 16)…

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Q: Write the standard equation of parabola with the focus at (-1, 2) and the vertex (1,2) Determine :…

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Q: Determine the standard form of an equation of the parabola with focus (1, 2) and directrix x = 7.

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Q: Write the Equation of the parabola: Focus: (0,5), Directrix: y= -3

A: We have to find the equation of parabola

Q: The foci of a hyperbola are (-4, 5)and (2, 5). What is the x- coordinate of the center of the…

A: Given:  Foci of a hyperbola   are -4,5   and 2,5To find:-   X‐coordinate  of the center of hyperbola…

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

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Q: Use the information provided to write the standard form equation of the hyperbola. Show your work…

A: We have to find the standard form of the hyparbola from the given data.

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

A: If (a,b) is the focus of the parabola,  and directrix is y = k,then strandard equation of parabola…

Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (0,…

A: Given:

Q: Make canonical equations for a hyperbola with an imaginary axis equal to 2 and focus F (-√13; 0)

A: One focus of the hyperbola is given.From the focus, the hyperbola is right -left facing…

Q: i: (6, –4), (–4, –4) jugate Axis is 8 units long

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Q: 5.) Vertex: (-2,4); Focus (-2,6) hk

A: As per the guidelines; we are supposed to solve only one problems from the given multiple questions.…

Q: Part 1 Find the equation of a hyperbola with center at (0, 0), focus at (0, -4), and vertex at (0,…

A: We will use standard form of equation of hyperbola.

Q: What is the Equation of a Parabola with directrix x = 3/2 and focus (5/2 , 4)

A: The given problen is solved below in detail.

Q: Example: Find the focus and directrix of the parabola y? = 10x. %3D

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Q: Find the standard form of the equation of the parabola with the given characteristics. focus: (5, 5)…

A: Answer and explanation is given below

Q: Write an equation of the parabola in standard form when focus is (9,0) and directrix is x=-9

A: The equation of parabola having directrix x=aand focus (a,0) is given by=y2=4ax

Q: Derive an equation for the parabola with focus (a , b) and directrix x = c

A: Given focus f =(a,b) and directrix x=c Let A(x1,y1) be any point so that  |Af|= |AD| Where Af=…

Q: The parabola has focus (0,-2) and directrix y=2.

A: equation of parabola with focus ( a , b ) and y = c  is given as below : here a = 0 b = -2  c = 2

Q: Determine the equation of the parabola, focus (-3/2,3) and directrix at x=-37/2.

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Q: Write the equation for a parabola with a Focus (4,1) and Directrix y=8 ?

A: we know that the distance between any point on parabola and the focus is same as the distance…

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: Write the standard form of an equation of a parabola with focus (1, 6) and directrix y = −2.

A: Given that focus and directrix of parabola.Find the equation of prabola in standard form.

Q: Find the parabola's focus and directrix. Then sketch the parabola. 2= - 8y %3D

A: The standard form of equation of parabola is (x-h)2=4p(y-k) where (h,k) is the vertex. The focus of…

Q: Find the standard form of the equation of the parabola with the given characteristics. Vertex: (3,…

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Q: Exercises 45–48 give equations for parabolas and tell how many units up or down and to the right or…

A: We’ll answer the first question (with complete information)  since the exact one wasn’t specified.…

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.