A spotlight uses a parabolic reflector, a surface with a parabolic cross-section, and a lightbulb at the focus of the parabola. If the bulb is 2 inches away from the vertex reflector, what is the equation of the parabola? Show your work and explain your reasoning.

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

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

A: We have to consider the parabola with vertex V whose coordinates with respect to XOY system is 0,0…

Q: find the equation of the parabola with the given properties.  Vertex (0, 0), focus (0, 2)

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Q: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

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Q: or the given equation of a parabola, determine the focus, vertex, and directrix. (x – 3)? = 32(y+ 4)…

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Q: satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: A satellite dish is shaped like a paraboloid of revolution. The receiver is to be located at the…

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: The mirror in an automobile headlight has a parabolic cross-section with the light bulb at the…

A: Equation of the parabola is given as x2 = 4y   Given that the headlight has a parabolic…

Q: suppose that the bulb of a flashlight is placed at the focus of its parabolic reflector. if the…

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Q: Find the focus and directrix of the parabola with the given equation. 4) 9x2 = -5y

A: Compare standard equation of parabola

Q: What is the equation of the drawn parabola? Notice that the green dot near the "f " marks the…

A: We can draw graph

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

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Q: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: Given:  An object is shaped like a paraboloid of revolution and its receiver is located at the…

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

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

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Q: A satellite dish is being designed so that it can pick up radio waves coming from space. The…

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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: Find the vertex, focus, directrix, and axis of symmetry of the parabola. (y+3)²=2(x-4)

A: Given, The parabola y+32=2x-4  We have to find vertex, focus, directrix and axis of symmetry of the…

Q: Find the standard form of the equation of the parabola with the given characteristics. y 1아 Vertex…

A: The equation of a parabola in vertex form: y=(x-h)2+k  Where the vertex is at (h,k) and the focus is…

Q: Find the equation of the parabola with the given properties Vertex (0,0), focus (5, 0). = x

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

A: To identify the type of the parabola, plot the point of its vertex and focus on the cartesian…

Q: Is it possible for two different parabolas to have the same focus and vertex? Explain with proof.

A: Actually, there cannot be two different parabolas with same focus and vertex..

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

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

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Q: One section of a suspension bridge hangs between two towers that are 50 feet above the surface and…

A: To find: The equation of the parabola that is shown in the given figure.

Q: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: It is given in the question that for x=64(end-to-end), y=8. Assuming the general equation of the…

Q: Find the standard form of the equation of a parabola with focus (8,0) and directrix x = -8.

A: Focus is, a, 0=8, 0⇒a=8 Directrix is x=-8.

Q: Find the standard equation of the parabola which satisfies the given conditions. Vertex (−4,2),…

A: Let the vertex V (-4,2) of the given parabola is left to the focus F(-4,-1) of the parabola. The…

Q: satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: Given: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed…

Q: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

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Q: The equation of the family of parabolas with vertex and focus on the x-axis where h and k are…

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Q: A parabola has a vertex at the origin and a focus of (0, 3). What is the equation of the parabola.

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Q: In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 50…

A: The general equation of a parabola opening downwards and having vertex at the origin is given by y =…

Q: Find the vertex, focus, and directrix of the parabola (x-3)2=12(y+1) and sketch the graph of the…

A: The graph of given parabola is graphed in the step 2.

Q: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: Given: A satellite dish is shaped like a paraboloid of the revolution. this means that it can be…

Q: An arch is in the form of a semi-ellipse, with its major axis as the span. If the span is 80 feet…

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Q: In order to hear what is said in a football huddle, a listening device is set up on the sideline. It…

A: Given that, In order to hear what is said in a football huddle, a listening device is set up on the…

Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y? - 8x + 16…

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

A: It is given that the towers supporting the cables are 800 feet apart and 100 feet high and it is…

Q: Find the standard form of the equation of the parabola. Vertex at the origin, focus at (2, 0)

A: General equation of horizontal parabola is given by -y-k2 = 4px-h             ..........(1)where, h,…

Q: Write the equation for a parabola with a focus at (-6,0) and a directix at x=-2

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Q: Find the equation of the parabola with focus (2, –1) and vertex (2, 3).

A: Given; Focus (2,-1) and vertex (2,3).

Q: the focus of the parabola and the directrix

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

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Q: 3. Find the equations of the parabolas that share a vertex and a focus with the ellipse 225 – 9x? -…

A: Given Equation of ellipse, 225-9x2-25y2=0

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.