Fit a Parabola. a) Find the equation of the unique parabola that passes through the three points (random). You must show all the algebra necessary to find the equation. b) Use substitutions to verify that each point satisfy the equation you found. c) Prints out the graph of this parabola and on the graph locate the three points. Also print out a table that shows the coordinates of the points using your function.

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

A:

Q: 5. What point is the vertex of the parabola?

A: The vertex of a parabola is the point where the parabola crosses its axis of symmetry.   If the…

Q: Using the graph, determine the coordinates of the roots of the parabola.

A: Given,

Q: Construct an equation for the following parabola.

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

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Q: Examine this parabola and determine the solutions.

A: given parabola :

Q: . Write the equation into the standard form of the equation of the parabola: x2 + 4x – 4y = 0.…

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Q: For Exercise, write the standard form of the equation of the hyperbola subject to the given…

A:

Q: An artist bends a long plank of wood into the shape of a parabola. The horizontal distance between…

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Q: II. Determine the vertex, focus, and the length and endpoints of the latus rectum. State the…

A: Given that: 12. (y+1)2=x-413. y2+x-10y+17=014. -x2-6x+y-4=0     NOTE: As per our answering…

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4.

A: We have to find the equation of parabola. Given data is  Directrix: y=3 Axis: x=0 Latus rectum: 4…

Q: Using the graph, determine the coordinates of the roots of the parabola. y 10 8 5 4. 3 1 -10 -9 -8…

A: Roots of the function from the graph

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

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Q: Plot the given parabola on the axes. Plot the roots, the vertex and two other points.

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Q: Find the standard equation of a parabola that has a vertical axis and satisfies the given…

A: Given:To Find the standard equation of a parabola that has a vertical axis and lineformula of…

Q: 6. Write the equation of the parabola in vertex form that has a the following information: Vertex:…

A: The standard form of a parabola with axis of symmetry parallel to x-axis is given by y-k2=4px-h with…

Q: In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the…

A: Here, the vertex is located at the lowest point of the cable. Let us take the horizontal line…

Q: Use the given information to write the equation of the parabola.

A: Since the directrix is y=3, So then the foci will be (0,-3).   Find equation of parabola on y- axis:…

Q: Given the parabola y = -2x² -8x+9. State the Range. (draw a sketch if necessary)

A: The range of a function, f(x) is the set of all output values of the function for which the function…

Q: Graph the parabola y = -x? – 2 by plotting any three points on the parabola. Move the key points to…

A: Given parabola equation y=-x2-2

Q: ph the parabola and find its vertex and axis of symmetry.

A: Solution of the problem as follows

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: solve for the equation in standard form then graph -Parabola with ?+1=0 as the directrix, ?=1 as…

A: To solve the given equation in standard  form and then plot the graph.

Q: Given the parabola y =-2x-8x+9. State the Range. (draw a sketch if necessary)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Using the graph, determine the coordinates of the roots of the parabola. 10 6. 8- 7. 9. 4. 2 -8 -7…

A: We have to determine the coordinates of the roots of the parabola using the graph.

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: An engineer designs a cable of suspension bridge that hangs in the form of a parabola, the towers…

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Q: Determine whether the given statement makes sense or does not make sense, and explain your reasoning…

A: It is given that, "I threw a baseball vertically upward and its path was a parabola."

Q: Using the graph, determine the coordinates of the roots of the parabola. 10 6. 6 10 "4 t3 -2 6. -2…

A: we have to determine the coordinates of the roots of the parabola  from the given figure.  For this…

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: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Plot the given points line joining focus and vertex is parallel to y axis. That means axis is…

Q: (a) What are the coordinates of the vertex of the parabola? Use of the grid below is optional. (b)…

A: We are given directrix y=4 and focus (-1,-2). We will use basic definition of the parabola to find…

Q: For Exercise, write the standard form of an equation of a hyperbola subject to the given conditions.…

A: Given:Vertices: (4, 0), (−4, 0); Foci: (5, 0), (−5, 0)

Q: . All parabolas with x-axis as the axis and (a, 0) as focus.

A: In this question, concept of differential equation is applied. Differential Equation A differential…

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (+11, 0), vertices:…

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Q: 6. State the coordinates of the vertex and the equation in star given the equation of parabola y =…

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Q: Find an equation of the parabola that satisfies the following conditions Vertex V (-3,5), axis…

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Q: For Exercise, write the standard form of an equation of a hyperbola subject to the given…

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Q: Find the vertices and foci of the ellipse: 6. (x-1) (y+3)? = 1. Round to nearest tenth if…

A: Given- x-129+y+3236=1 To Find- The vertices and focii of the ellipse.

Q: Use the information provided to write the equation of each parabola. 33 17) Vertex: (6, -8), Focus:…

A: Note: as per our guidelines we are supposed to answer only one question.* *Kindly repost other…

Q: Write the standard form of the equation of the parabola that has the indicated vertex and passes…

A: GIven information: The vertex of the parabola is -3,4 and the point is 0,13. The general equation of…

Q: b. Find another equation of the parabola with vertex of coordinates 131 and containing the point of…

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Q: Given the parabola y =-2x -8x+9. State the Range. (draw a sketch if necessary)

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Q: Find the standard form of the equation of the parabola satisfying the given conditions. Foci: (2,4)…

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Q: Find the standard equation of a parabola that has a vertical axis and satisfies the given…

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Q: Determine the standard form of the parabolic equation x = 1/2 (y + 5)2 − 2. Further, characterize…

A: x=12y+52-2 On simplification, we get ⇒12y+52=x+2⇒y+52=2x+2⇒y--52=2x--2 Now it is in the form of…

Q: Determine the equation of the parabola shown.

A: From the given equation of the parabola, the graph crosses the x-axis at two points which are x = -5…

Q: Find the vertex and length of the latus rectum for the parabola. y = (x - 2)2 - 9 Vertex: (x, y) = (…

A: Topic = Parabola

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.