Find the D.E. of the family of parabolas with axis parallel to the y – axis and with the distance from focus to vertex fixed as a. а. а(у)? 3 у c. 1= 2ay" e. none of the choices b. a = x(y')² d. (y)³ + 2ay" = 0

Q: What is the nearest distance from the point P(6,0) to the parabola? y^2=8x

A: GivenP(6.0)y2=8x To find nearest distance

Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

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Q: Describe the part of a hyperbola given by the equation.

A: Given equation is  x=23y2-36

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

A: Given that, vertex of parabola is (h, k) = (0, 0) diretrix of parabola is, y = -8 We have to find…

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

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Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

Q: Find the equation for the parabola that has its focus at the (−394,−4) and has directrix at x=−25/4

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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: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: 9. Find the equation of the parabola that had vertex at (4,-2) and focus at (6,-2)

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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: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: What is the standard equation of the hyperbola if the length of its transverse axis is 12 and one of…

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Q: Suppose you are given the x-coordinate of a point on a parabola. How can you find the matching…

A: According to Bartleby guidelines, only one question can be solved at a time. Kindly post other…

Q: 16. Which equation represents a parabola with vertex (4, 4) and directrix y = 2? O y = 2a2 - 4x + 4…

A: We need to find the equation of parabola whose vertex is (4,4) and directrix is y = 2

Q: 5. If graphed, which of the following parabolas would lie entirely below the x-axis? (1) y=x² +5x+10…

A: We’ll answer the first question  . Please submit a new question specifying the one you’d like…

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: 5. Identify the focus of the parabola given by y = 8x². O (0,) O (-8,0) O (0,0) O (8)

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Q: Fit a second degree parabola to the followng aata : 1 2 3 4 1 1.8 1.3 2 6.3

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

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

A: Given: Focus on the negative y-axis, 6 units away from the directrix

Q: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: 4x + y2 + 8y + 8 = 0   If it is a parabola, find the vertex, focus, and directrix.

A: As a first step we will convert the equation in the standard form of equation representing a…

Q: 1. A parabola with directrix y = 51 59 and one endpoint of the latus rectum at (--) 32

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Q: Show that the graph of an equation of the formAx2 + Cy2 + F = 0 A ≠ 0, C ≠ 0, F ≠ 0where A and C are…

A: Consider the given equation Ax2+Cy2+F=0, A≠0, C≠0, F≠0 A and C are opposite in sign. So,…

Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: Graph the parabola with a focus of ( – 2, 1), a directrix of y = 7, and goes through the point (4,…

A: We have to find the equation of parabola.

Q: Given a parabola with vertex at (8,-4) and focus at (-4,-4), determine the equation of the parabola.…

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Q: 2. Find the equation of the parabola described. a. Vertex at (4, –2); focus at (6,–2) b. Focus at…

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Q: What is the equation of the standard hyperbola with vertices at (0, ±a) and foci at (0, ±c)? Choose…

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Q: What is the equation of the parabola with vertex at (0,0) and focus (0, –4) in standard form?…

A: see below the calculation

Q: if the point (a, b) is on the parabola y=6x^2-(5785/12) that is closest to the point (0,4) than a ?

A: Given, y=6x2-578512 suppose x,y any point closest to 0,4  D=x-02+y-42 put y in equation,…

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

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Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: Do the following for the points (-5, 2), (0, 1), (1,-2), (3, 2), (4,-2): (If you are entering…

A: Given

Q: d the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)…

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Q: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

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Q: Which of the following represents a parabola with vertex at (4, -2) and focus at (4, 4)? O A. (x -…

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Q: Find the equation of Hyperbola using only the following information: Center at (0, 0) Vertices at…

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Q: The parabola y=x^2y=x2y, equals, x, squared is shifted up by 777 units and to the left by 111 unit.…

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Q: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

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Q: Find the equation of the hyperbola that is centered at (0,0), has vertices at (t10,0) and has 6.…

A: Consider the given values. Center=0,0vertices=±10,0y=±65x The gerneral equation of hyperbola with…

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: (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 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: 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: 1. Which of the following best describes the graph of y = x? – 4x + 2? a parabola with a vertex at…

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Q: Two parabolas are given: - C₁ is the curve of intersection between y = 1-2² and 2 = - C₂ is the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 4. What is the focus of the parabola whose equation is -(y- 3)2 = (x – 2)? O A. (2, 1) OB. (0, 3)…

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