10. A satellite dish measures 10 feet across its opening and two feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where should the receiver be placed? (Hint: Consider modelling this with a parabola whose vertex is at the origin and whose axis of symmetry is at x = 0.)

Q: Given the general form of a parabola x2+6x-32y+10=0, what is the x coordinate the focus? (round to 1…

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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: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = -8 in standard form?…

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A: According to the given information, it is required to find the maximum and minimum value of the…

Q: Given a parabola's focus at (6, −4) and directrix at y = −7, how would you write its equation?

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

Q: What is the measure of the focal width of the parabola y+2y+4x-3=0 ?

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Q: A ship is following a course that is 104 miles from and parallel to a straight coastline. The ship…

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Q: 3. Write an equation for the parabola with vertex at (2, 3), opening upward, and with no vertical…

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Q: Consider the point P (-1,0)on the ellipse 4x2 + y? What is the value of a? Answer to 3 significant…

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

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Q: 1. Use the focus-directrix definition of a parabola to answer the following questions. 1) How would…

A: (1) When the focus is moved up the parabola opens wider, in other words as the parabola gets…

Q: The Golden Gate Bridge has a main span of 4, 200 feet and two main cables that hang down 500 feet…

A: Given that the Golden Gate Bridge has a main span of 4200 feet and two main cables that hang down…

Q: 2. Parabola with x+1= 0 as the directrix, y = 1 as the axis, and the length of the latus rectum is…

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

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Given: Opens downward with focus 10 units away from the vertex.

Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

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Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

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Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: 5. Sketch the parabolas showing the intercept and the maximum/minimum points. a) y = 2x – 4x +7 b)…

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Q: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

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Q: Given hyperbola   (y + 1)2   −   (x − 2)2   = 1       9                4         what will its…

A: Given: An equation of the hyperbola, y+129-x-224=1.

Q: 17. Parabolas with axis parallel to the x-axis and with distance from vertex to focus fixed as a. Am…

A: This question is about family of parabolas.

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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: 5. The equation of a family of parabolas with axis paralel to the y-axis is

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Q: 1. Find the maximum and minimum distance from the origin to the ellipse 2² + xy + y² = 3

A: 1) To Find: The maximum and minimum distance from the origin to the ellipse x2+xy+y2=3. As per…

Q: Given hyperbola   x2   −   y2   = 1   9         16       how do you determine the focal length?

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Q: satellite dish shaped like a paraboloid, has a diameter 2.4ft and depth 0.9ft. If the receiver is…

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Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: What is the standard form of the equation of the parabola with the focus (1, –3) and the directrix x…

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Q: Find the shortest distance +rom the point (0,5)to the ellipse 3 y? = x'

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Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2 Ans: 2xy" - 4yy"…

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Q: 4. Find the area of the largest isosceles triangle that can be inscribed in the ellipse y2 = l. a2…

A: To find the area of the largest isosceles triangle.

Q: 24. Construct the equation of a parabola with focus at (-1,2) and a directrix x = -7.

A:

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…

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Q: 1. Consider the parabola whose directrix is at x = -7 and whose focus is at (-1, 1). What is the…

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Q: The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of…

A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

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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: (a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph…

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Q: What is the equation of the directrix of a parabola having vertex at (4, 3) and focus which is 2…

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through from the hoop is modeled by the parabola,

Q: If a parabola's focus is at (-2,5) and directrix is at y = -1, what is the vertex form of the…

A: The correct answer is option (2).

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x ^ 2, for −1…

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Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = 3 in standard form.…

A: Given vertex 0,0 and directrix y=3. We have to find equation of parabola.

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: 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: Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0).

A: