1) What is the orientation (Horizontal or Vertical) of this parabola? Where is it opening? 2) Identify its vertex, focus, and equation of the directrix. How far is the focus from the vertex?

Q: 2. Given the stated information: Foci at (-5,0) and (5,0); length of the major axis is 12 units a.…

A: (2).   (a). Given: Foci of the ellipse: (-5, 0)  and  (5, 0) Therefore the center of the ellipse is:…

Q: In an ellipse, the foci are at (-4, 3) and (4, 3) and one vertex is at (6, 3). How long is the major…

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Q: = 18 , find the co-ordinates of the vertices, foci, equations of the For the hyperbola 9Y² – 2X?…

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Q: Find the coordinates of the foci and vertices, the endpoints of the major axis, minor axis, and the…

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Q: 21. What are the vertex, focus, and directrix of the parabola with equation y = x- 6x + 15?

A: Here we have to find the vertex, focus, and directrix of the parabola with the equation y=x2-6x+15

Q: For a hyperbola, the foci lie on a line called the_________

A: Given that, A statement, " For a hyperbola, the foci lie on a line called the ______ ."

Q: Explain why the dots in the Figure given below lie on a parabola. Where are the focus and directrix…

A: the figure in the diagram is a circle so It should be in the form of x2+y2=K Now y =c or some…

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (+5, 0), vertices:…

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Q: Solve for the equation of the parabola described. Vertex at (2,4); focus at (2,-1)

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: 2. Consider the parabola whose equation is (x + 5)2 = -16(y – 7). What are the coordinates of the…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 3. GIVEN: HYPERBOLA WITH CENTER FOCUS VERTEK FIND: EQUATION

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Q: The distance from the center of a hyperbola to its vertex is larger than the distance from its…

A: Given query is to find that statement is true or false.

Q: Find the vertex, focus, directrix, and focal width of the parabola. x2 = 28y

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Q: The circle, the ellipse, the hyperbola, and the parabola are categories of _____ sections.

A: The intersection of a plane and a double napped cone is known as conic sections.If the set if…

Q: Communicate Precisely How can you find the focus of parabola given the vertex and the directrix?

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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: 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 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: 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: Find the center, foci, vertices, and eccentricity of the hyperbola                         ( y +…

A: y+32225-x-5264=1⇒y--32152-x-5282=1 Now comparing with y-k2a2-x-h2b2=1, we get k=-3, h=5, a=15 &…

Q: What is the directrix of a hyperbola?

A: We need to explain what is meant by directrix in hyperbola and find its equation.

Q: A cable TV receiving dish is in the shape of a paraboloid of revolution (3D parabola). Find the…

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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: The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints…

A: Given:The line segment perpendicular to the axis of symmetry, passing through the focus and with…

Q: The cables of a suspension bridge are in the shape of a parabola.The towers supporting the cable are…

A: A parabola is a type of curve which where the distance of any point of the curve is same from one…

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

A: All vertices and foci are on the x-axis so the equation of the hyperbola has the standard form:

Q: One of the most important applications of parabola are their reflective properfties. Light rays…

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Q: A lamp has the shape of a parabola when viewed from the side. The light source (which is at the…

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Q: focus shaded region has area 8

A: we know that equation of parabola is given by x2=-4ay where, focus is 0,-a, vertex is 0,0 and…

Q: Find the vertex, focus, and directrix for the parabola.

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Q: What is a hyperbola? What are the Cartesian equations for hyperbolas centered at the origin with…

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Q: 2. Find the equation of the parabola described. a. Vertex at (4, –2); focus at (6,–2) b. Focus at…

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Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola 15.6x = y?

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Q: 1. Give the focus and directrix of the parabola with equation x? indicate the focus, directrix,…

A: Given: x2=10y

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: (b) What can you say about the eccentricity if the conic sectionis an ellipse? A hyperbola? A…

A: Eccentricity- The eccentricity of a conic section tells us about its shape, it shows how much a…

Q: 9. How is the equation of a hyperbola different from the equation of an ellipse?

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Q: If the directrix is horizontal, then the parabola opens (horizontally/vertically).

A: Given:We must find the missing word in the given sentence.So, Definition of parabola said:A parabola…

Q: How are the graphs of these ellipses similar and how are they different? are = 1 (x – 1)?, (v + 7)²…

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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: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±13), vertices:…

A: Given that, Foci: 0, ±13 Vertices: 0, ±4 This hyperbola is the type where the line drawn to its…

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: car is traveling at night along a highway shaped like parabola with its vertex at the origin (see…

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Q: What equation is used to find the foci of a hyperbola?

A: The hyperbola which is having transverse axis along x-axis is given by x-h2a2-y-k2b2=1 where h,k is…

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

A: Given that, The casting has a depth of 2 inches that is y = 2 in. And the casting has a diameter of…

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 equation for the parabola that has its vertex at the origin and has directrix at a The…

A: Given that, Vertex of the parabola are, (h, k) = (0, 0) And diretrix of parabola is x = - 12 We have…

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, +9), asymptotes: =…

A: Given foci (0,±9) , asymptotes y=±12x let’s find an equation of hyperbola