1. Determine the foci, vertex, and directrix of the parabola with the given equation. (a) x2 = 10y (b) 2y2 = 16x (c) (x + 3)2 = 4(y- 1) (d) x2 – 8x -8y = 0 (e) 2y2 - 6x - 4y = 1 %3D | %3D %3D

Q: Sketch the graph of the hyperbola 4x2 − y2 = 16.

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Q: 1. Find the equation for the parabola that has its vertex at the origin and has directrix at y = 25…

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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: Find a function whose graph is the lower half of the hyperboloid -x2 - y2 + z2 = 1.

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Q: 14. Consider the equation: y -8x+2x² –6y+13=0 (a) Show work to determine whether this equation…

A: Given : y2-8x+2x2-6y+13=0

Q: B. Determine the center and orientation of the principal axis of each hyperbola. 1. x2 - y2 - 1 4 5…

A: Three equations of hyperbola are given. We have to find the center and orientation of the principal…

Q: transform into standard form of hyperbola x^2-y^2+6x-4y-4=0

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Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

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Q: 9. Find b and c so that the parabola y = -3x? + bx + c has intercepts 1 and – 4.

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Q: Find an equation of a hyperbola satisfying the given conditions. Vertices at (1, - 5) and (1,3);…

A: The general equation of conic section is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. The standard form of the…

Q: Sketch the hyperbola 9x² – 4y² – 18x + 8y – 31 = 0, and label the center, foci and vertices. Find…

A: Given : 9x2-4y2-18x+8y-31=0

Q: 17. What is the center of the hyperbola whose equation is [(x+3)2 / 9] - [(y-3)2 / 16] = 1?

A: The given equation of the hyperbola is of the type [(x-h)²/a²]-[(y-k)²/b²]=1.

Q: transform into standard form of hyperbola 4y^2-9x+16y+18x-29=0

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Q: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

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Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: 1. Find the general equation of the parabola with vertex at (-2,3) and focus at (-2,–2). 2. Graph…

A: 1. The given vertex at -2,3 and focus at -2,-2. Find the general equation of the parabola. 2. The…

Q: What are the coordinates of the vertices of the hyperbola whose equation is given by 4y2 – x² = 4? A…

A: The given hyperbola equation,        4y2-x2=4

Q: 17. If the focus of the parabola is (-2, 1) and the directrix has the equation x + y = 3 then the…

A: Given Focus of parabola f (-2, 1) Equation of directrix is x+y =3   Here the objective is to find…

Q: 1. Give the coordinates of the center, foci, vertices, and the asymptotes of the hyperbola with the…

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Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

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

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (±1, 0),…

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Q: 2. Suppose that the equation Ax + Bxy + Cy² + Dx + Ey + F = 0 represents a conic section…

A: The equation Ax2+Bxy+Cy2+Dx+Ey+F=0 represents a conic. If B2-4AC>0 , The conic represents…

Q: The point (1,2) lies on the parabola: y 3x2 -2x+2 %3D

A: Thanks for the question :)And your upvote will be really appreciable ;) False statement (1,2) does…

Q: Determine the vertices of the hyperbola. (y - 3)2 - (x + 5)2 = 1 4 9 (х, у) %3D (smaller y-value)…

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Q: 5. What is the standard for equation of a parabola with its vertex at (0,0) and a directrix of x-3?…

A: Given: A parabola has vertex 0, 0 and directrix x=3      ……1   To find: Equation of parabola

Q: Find the foci of the hyperbola. 2 4x-y- 2 32x+ 28 = 0

A: See attached file for a step by step explanation to find the foci of the hyperbola.

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

Q: Find the equation of the hyperbola with vertices at (-4,2) and (0,2) and foci at (-5,2) and (1,2).…

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Q: the parabola x^2-4x-4y=0

A: we have to find the vertex , focus and directrix of the given parabola. x2-4x-4y=0

Q: Find the length of the hyperbola. (y-2)2/ 9 - (x+1)2/4 =1

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Q: How to convert 3y^2-x^2-9=0 into standard form? I know it is a hyperbola.

A: Answer and explanation is given below..

Q: Find an equation of a hyperbola satisfying the given conditions. Vertices at ​(1​,−7​) and ​(1​,1​);…

A: Given that the Vertices at ​(1​,−7​) and ​(1​,1​). So the center will be at the midpoint Center=…

Q: 5. Find the equation of the hyperbola whose asymptotes are the straight lines x = 0 and y = 0 and…

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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: Consider the equation of parabola y = 5x - 30x + 45. %3D Its vertex is located at (

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Q: Find the standard equation of the hyperbola with the stated conditions. Vertices at (2,-5) and…

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Q: Find the equation of a hyperbola whose vertices are (+2,0) and whose foci are (+5,0). x2 A) 4 = 1 21…

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Q: What is an equation of the axis of symmetry of the graph of the parabola y = 2x² + 3x + 5? A y=-} O…

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Q: İThe hyperbola with vertices at (0, 3) and (0, - 3) and foci at (0, 5) and (0, - 5) has the equation…

A: The objective of the question is determine the equation of the hyperbola and choose the correct…

Q: 1. Draw the hyperbola with the equation: 3x^2-2y^2+6x-8y=6.

A: The standard form of hyperbola 3x2-2y2+6x-8y=6 is, x+1213-y+2212=1. Comparing above equation with…

Q: 4. Determine whether a hyperbola exists if it has an equation of x2 - y2 + 6x +36y = 18.

A: we have to determine whether a hyperbola exists if it has an equation of  x2-y2+6x+36y=18

Q: 19. What is the equation of the horizontal asymptote for this hyperbola ? y = (6x + 8) / (3x - 2) *

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Q: The graph of y^2 = x^3 is called a semicubical parabola. Determine the constant b so that the line y…

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Q: What is the equation of parabola with vertex at (-2,0) and focus at the intersection point of the…

A: Given: (x+2)^2=-16y-64 and (x+2)^2=16y+64

Q: 9. Find an equation of the parabola that satisfies the given condition: Vertex V(-1,0) and focus…

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Q: Which is the equation of a hyperbola with co-vertices at (0, 7) and (0, −7) and a transverse axis…

A: Ans (1) we have givenCo=Vertics of hyperbola (0,7) and (0,-7)⇒Compairing with co-vertice from (0, ±6…

Q: 3 (a) Express the equation of the parabola y' -8x-4y-20 0 in standard form. Hence, find the vertex,…

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Q: 2. Find the equation of the hyperbola whose asymptotes are perpendicular to the lines 5x – 4y +9 = 0…

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