Some comets, such as Halley's comet, are a permanent part of the solar system, traveling in elliptical orbits around the sun, other comments pass through the solar system only once, following a hyperbolic path with the sun at a focus. The figure shows the path of such a comet. Find an equation for the path, assuming that the closest the comet comes to the sun is 2 x 10^9 mi and that the path the comet was taking before it neared the solar system is at a right angle to the path it continues on after leaving the solar system.

Q: Please provide 3 real-life word problems with solutions and explainations regarding conic sections…

A: Please see the below pictures for detailed solution.

Q: Write an equation for each hyperbola.

A: From the figure of the given hyperbola, find out the vertices , co-vertices and the center of the…

Q: Create the equation of a parabola passing through the points (-2,32), (1,5) and (3,17)

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Q: determine the equation of this parabola

A: The general form of the parabola is y=ax-h2+k where h,k is the vertex of the parabola.

Q: Write the equation of the hyperbola in standard form. 10 (-6, 2) (4,2) (12,2) • (-14,2)

A: Vertices of hyperbola are, h-a, k=-6, 2  &  h+a, k=4, 2⇒h-a=-6,  h+a=4  &  k=2⇒h=-1,  a=5…

Q: Write an equation for each parabola.

A: Let's assume equation of parabola is  y=ax2+bx+c…

Q: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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Q: Write the equation of the hyperbola in standard form. 10 (-14, 2) (-6, 2) (4,2) (12, 2) 15 -10

A: Solution:GivenTo find the Equation of hyperbola in standard formFormula:(x-h)2a2+(y-k)2b2=1

Q: Write the equation of a parabola in standard form from the given information Vertex at (2, -2)…

A: Vertex of the parabola is at 2, -2 and focus at 2, -3. Now vertex is, h, k=2, -2⇒h=2  &  k=-2…

Q: Find the equation of the parabola whose graph is given below.

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Q: Write an equation for the parabola whose vertex is at (3, 6 ) and which passes through point (4, 4…

A: Given Data: The vertex of the parabola is: (h, k)=(3, 6) The coordinate of a point on the parabola…

Q: Write an equation for the parabola shown. 10- (2,5) (3,4) -10 10

A: You must have an idea about the basic parabolic functions and its transformations.

Q: Write an equation for the parabola shown to the right. (3, 1) (2, 0)

A: The equation of parabola in vertex form: y=a(x−h)2+k where: h is the horizontal coordinate of the…

Q: A hawk flying at 15 m / s at an altitude of 180 m accidentallydrops its prey. The parabolic…

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Q: According to the figure, find the equation of parabola: - 2 (-2,1) -5

A: (y-k)2 = -4a(x-h) is a equation of parabola opening in negative direction of x-axis. (h,k) is vertex…

Q: Can you do a parabola with the starting point being (0,0)

A: Given a parabola with equation y=x2

Q: The Arecibo Observatory in Puerto Rico was just decommissioned after sustaining a lot of damage, but…

A: It is given that, the height of the focus from the vertex is 500 feet and it is 1000 feet wide at…

Q: Find the equation of a parabola whose vertex is located at (2, −3) and whose focus is located at…

A: Given: vertex: 2,-3focus: 0,-3 To Find: Equation of a parabola. Concept: Horizontal…

Q: Find the equation of the parabola

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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: Write the standard form of the equation of a parabola with directrix of x = -10 and vertex at (-6,…

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Q: Write the equation of a parabola with vertex (0,0) and directrix y =-3

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Q: Give 1 word problem with solution about hyperbolas in a guitar

A: The place where the outside of the guitar dips in, those dips make the sound of a guitar echo.

Q: Find the equation of a parabola whose latus rectum is joined by points (2, 1) and (-4, 1)

A: Use equation of parabola

Q: Write the equation of the hyperbola in standard form. | (-1,7) (-1,5) (-1,1) (-1,–1)

A: We can see from the graph,Vertices of hyperbola = (h, k ± b) = -1, 5 & (-1, 1)h = -1k + b = 5…

Q: If it is projected to be out of the Philippine Area of Responsibility in a few days given an…

A: Standard form of a circle, x-h2+y-k2=r2 Where (h, k) is a center of a circle and r is a radius.

Q: Find an equation for the hyperbola whose graph is below. 4- -8-6 -2 -4- 6.

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

Q: Write the equation of the parabola in standard form

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Q: Find the equation of a parabola that lies through (3,3), (-4,3), (1,7)

A: To Determine: Find the equation of a parabola that lies through (3,3), (-4,3), (1,7) Given: we have…

Q: Write an equation for the hyperbola with vertices at (-4,0), (4,0) and passing through (20,1).

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

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Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A: Given:A golf ball travels a distance of 200 feet as  measured along the ground and reaches an…

Q: Correctly match up the vertex and axis of symmetry for this parabola.

A: We have to find the vertex and axis of symmetry according to the given information

Q: Determine the equation of the parabola given:

A: Graph of the hyperbola is given, we have to find its equation

Q: determine an equation for the blue parabola in standard form

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Q: Write an equation for the parabola shown to the right.

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Q: Write the equation of the parabola that has "a" value 2 and roots -1 and 4.

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Q: The center of a clock is 60cm above the ground. The minute hand on the clock is 23cm long and starts…

A: topic- trigonometric equations

Q: mark the vertex of the parabola

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Q: Find the standard equation of the parabola shown in the figure.

A: Consider a parabola passing through the points: (-4,0); (6,0) and (4,-4). Equation of parabola with…

Q: How can we Find the slope of the parabola?

A: Let the equation of a parabola be: y^2 = 4ax

Q: Find the equation of the ellipse with the major axis from (-9,2) to (1,2) and minor axis from (1,-1)…

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Q: Find an equation for the parabola shown in the figure.

A: Given: The focus F-2,1 and directrix x=3 of the parabola, To find: The equation of the parabola.

Q: -10어 -5-

A: Standard form of parabola when it is open toward positive x-axis is (y-k)2=4p(x-h) where focus is…

Q: Write the equation of the parabola in intercept form that has x-ints at 12 and -6 and passes through…

A: Given , x intercepts of a parabola are 12,-6.            Parabola passes through a point (14,4) We…

Q: Write the equation for a parabola with vertex: (-2, 4) and directrix: x= -3

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Q: Describe how the parabolas y = x2 + bx change as b changes from -oo to oo.

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Q: Write the equation of a parabola whose directrix is x 12.5 and has a focus at (5.5, – 9). -

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Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

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Q: Find the equation in standard form of a parabola whose focus is at (-3,-2) and whose directrix is x:…

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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.