A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x2=3y around its axis of symmetry (assume that x and y are in units of inches). In order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed? Express your answer as a fraction or a decimal rounded to two decimal places.

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: 3. The towers supporting the cable of a suspension bridge are 1200 m apart and 170 m above the…

A: Solution:-   First we are draw a rough diagram based on the given problem.      Both towers are…

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

A: We will solve the following.

Q: Show that when a satellite is in elliptical orbit, its speed V is given by v² = k = k ( ² − ²) and…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 12 –…

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Q: The quadric surface, * - a - = 1 l is a hyperboloid %3D 64 None of these of one sheet that opens…

A: The given quadratic surface is: x24-y264-z216=1

Q: Compute the length of the latus rectum of the parabola y2 + 8x – 6y + 25 = 0.

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Q: A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from…

A: A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from…

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A cooling tower, such as the one shown in the figure, is a hyperbolic structure. Suppose its base…

A: Let the tower be a hyperbola centered at the origin as shown in the figure. Since the lowest…

Q: In the xy-plane, if the parabola with equation y = ax² + bx + c, where a, b, and c are constants,…

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Q: 3) Fit a parabola to the data. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y 3.1950 3.2299 3.2532 3.2611…

A: the equation of the parabola is given by y=ax2+bx+c we have to use the calculator to find the…

Q: The maximum area of a parabola that can be inscribed in a right circular cone of radius 6 is 207.8…

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Q: 3) Fit a parabola to the data. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y 3.1950 3.2299 3.2532 3.2611…

A: A second-degree ee equation represents a parabola. The general equation of a parabola is y =…

Q: a. If a chord of the parabola y² = 4ax a normal at one of its ends, show that its mid- %3D y?, 8a3…

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Q: Find three points on the parabola. x^2−8x−8y−8=0

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Q: Find the vertex, force, and directrix of the parabola x^2=7y

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: 4. What is the axis of symmetry of the parabola y = x = 7 x= -14 y = 28 Ox=28 O x²14x+28?

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Q: The reflector of a searchlight is in the shape of a paraboloid of revolution. Its diameter is 16…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: 3. Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes…

A: Let vertex of the rectangle be x,y, x,-y, -x,y and -x,-y. Thus, are of the rectangle is fx,y=4xy. We…

Q: The reflector of a flashlight is in the shape of a paraboloid of revolution.Its diameter is 4 inches…

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Q: A geometry student wants to draw a rectangle inscribed in the ellipse x2+4y2=49. What is the area of…

A: For maximization, equate the derivative of the function to 0 to get the critical points.Then check…

Q: 4 SKetch the parabola and label the foces , ventees and dineder 2. 4 -6y -2utl=0

A: To find- Vertex, focus and directrix of a given parabola.

Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

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Q: The general form of a hyperbola is 6x – 5y + 12x + 50y – 149 = 0. - What is the standard form of…

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Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

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Q: A rectangular object 25 m wide is to pass under a parabolic arch that has a width of 32 m at the…

A: The arch can be modeled by the vertex form of a parabola centered at the origin with the base being…

Q: The centre of a circle C lies at the focus S of a parabola y2 = 4x and the radius of C is equal in…

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Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: The given equation of parabola is y2=4ax. The objective is to calculate the area bounded by the…

Q: 25 E. A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror…

A: If we draw the parabola used to form the mirror on a rectangular coordinate system so that the…

Q: Compute the length of the latus rectum of the ellipse x2 + 2y2 +4x+ 4y +4=0

A: Given:    x2 + 2y2 +4x+ 4y +4=0

Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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Q: Show the figure or model of a rectangular object 25 m wide is to pass under a parabolic arch that…

A: given that Parabolic arch has a width 32m at the base and height 24m at the center Vertex of…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1 –…

A: first we have to draw the sketch of y = 1-x2 and draw a rectangle beneath it From the graph we can…

Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: 9.  Find the shorted distance from point A(2, 1/2) to a point on the parabola y = x2. And find the…

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Q: It has been shown that when like particles with a common charge are hurled at each other, they…

A: Let's find.

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Vertices of parabolas = (0,0), Foci on the y-axis.

Q: A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and…

A: It is given that, A mirror for a reflecting telescope has the shape of a (finite) paraboloid of…

Q: A flashlight is shaped like a paraboloid, so that if its light bulb is placed at the focus, the…

A: Given :  The paraboloid has a depth of 1.8 in  and the diameter on its surface is 6 in .   Schematic…

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: A satellite dish is shaped like a paraboloid, with the receiver placed at the focus. It is to have a…

A: The base of the dish is the vertex of the parabola. The parabola is upward oriented. Let the vertex…

Q: Find the area of the fundamental rectangle of the hyperbola. x2 − y2 − 6x − 8y = 8

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Make equation of parabola

Q: Which of the following parabolas opens left with a vertex of (3, 2)? Oy = 2(x + 3)² + 2 Ox = -2(y -…

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Q: 3) Assume that the parabola y=x is translated so that its vertex is (5,-4). I If the parabola is…

A: Let's see a concept of stretch of function y=f(x). Say y = f(x) is parent function.

Q: Find the vertex Focus and divertrix to given the parabola x2 +6x+8y+25-0

A: The given equation is: x2+6x+8y+25=0 That can be written as…

Q: A parabolic arch has a height of 16m and a width of 28m atthe base, If the vertex of the parabola is…

A: As this is a multiple question according to the Bartleby Answering rule, only first question and its…

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.