Express the general form to its standard form and locate the center, vertices, covertices and foci of the equation 4x2 - y2 - 32x - 4y + 24 = 0

Q: Find an equation of the parabola with vertex (-2,-4) and directrix y=-9.

A: given vertex (h,k)=(-2,-4) h=-2,k=-4 directrix y=k-p=-9                  p=k+9                p=-4+9…

Q: Write the equation for the hyperbola with foci (-12, 6), (6, 6) and vertices (–10, 6), (4, 6). =1…

A: The hyperbola with foci (-12,6), (6,6) and vertices (-10,6), (4,6)

Q: Find the equation of a parabola that has a vertex of (-5, -3) and contains the point (-4, -5).…

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Q: Find the equation of the parabola in general form with vertex (-1,2) and focus (-1,–2).

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Q: Find the center, vertices, foci, and sketch from x -4y2 +6x +16y -11 = 0.

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Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: What are the coordinates for the vertex of the parabola y = 3x2 - 6x- 1? O (1,-4) O (1,4) 0(-1,4)…

A: answer is option A.)   explanation is given in below step

Q: find the coordinates of the vertex and the focus for the parabola given by x2+6x+24y-111=0

A: SOLUTION-

Q: Find the x-intercepts and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If there…

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Q: 2 4x + 9to vertex form by Change the standard form equation y = x" completing the square. -

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Q: 9. Sketch the parabola y =-x +8x-12, show all the intercepts, the axis symmetry and the vertex

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Q: Identify the center vertices, co-vertices, and foci of x2+9y2+6x-90y+225=0

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Q: Find the standard equation of the parabola which satisfies the given condition. Vertex (-8, 3),…

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Q: Find the coordinates of the vertex of the parabola y = 3x2 - 6x + 8

A: we have to find the coordinates of the vertex of the parabola y = 3x2 - 6x + 8

Q: Find the equation of the parabola with vertex (−3,1) and y-intercept 2(or (0,2)).

A: We have to find the equation of the parabola with vertex (−3,1) and y-intercept (0,2).

Q: Find an equation of the sphere whose endpoints of a diameter are (-2,0, 5) and (-1,2, 3).

A: To find the length of the diameter use the distance equation Therefore, D=-2-(-1)2+0-22+5-32…

Q: Find an equation of the parabola that satisfies the given conditions.Vertex V(3, -5), directrix x =…

A: We know that equation of parabola is, y-k2=4px-h       ...(1) Where (h, k) is the vertex and x = h -…

Q: Find the vertex of the parabola defined by the following equation: (y – 2)² = –4x – 8 - -

A: Given : y - 22 = -4x - 8

Q: use the method of completeing the sqaure to find the vertex of the parabola whose equation is…

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Q: Find an equation for the parabola with vertex (0, 0) and focus (6, 0).

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Q: Convert y = x + 12x +20 from standard form to vertex form. Only an algebraic solution will receive…

A: Given  y = x2 + 12x + 20  The given equation can be converted to the vertex form by the method of…

Q: 12. Use vertex form to write the equation of the parabola. y= 3(x+2)° +2 y= 3(x- 2)° +2 y= 3(x- 2)°…

A: best and easiest way is one by one checking if the given option satisfy the given points (-2, 2) and…

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: Find the vertex of the parabola. y = 3x² - 1 О (0, (0, –1) O (-1, 3) O (-1, 0) (3, –1) (0, 3)

A: topic - parabola

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: Complete the square to find the vertex of this parabola. x² – 12y – 6x + 5 = 0 3,-

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Q: Give 3 points that lie on the parabola y=x^2-5x-2

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Q: Find an equation of the sphere whose endpoints of a diameter are (-2, 0, 5) and (-1, 2, 3).

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Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

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Q: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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Q: State the vertices of the hyperbola. x² _ y² 1 4 25 (x, y) (smaller x-value) (х, у) %3D (larger…

A: We will solve the following.

Q: Find an equation for a parabola with vertex (3, – 6) and focus (3, – 1) -

A: We have to use general equation of parabola.

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

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Q: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

Q: Complete the square to find the center and radius: x^2+y^2+2x+4y-1=0

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Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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Q: Find the standard equation of any parabola that has vertex V.

A: V-2,0

Q: Determine the equation of the parabola vertex at (-4,-8) directrix is x=0.

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Q: Find the equation for the parabola with vertex (-3,0) and focus (0,0).

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Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

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Q: Determine the direction in which the parabola opens, and the vertex. y2-10y-x+23=0

A: Add x to both sides. So, this is a parabola of the form y=ax^2+bx+c with a=1=positive number. So…

Q: Find the point on the ellipse x2 + 3y + 2xy = 6 with the greatest x-coordinate. (Use decimal…

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Q: Write an equation of the parabola with its vertex at (x, y) - (3, 9) and focus at (x, y) (3,-2).

A: The parabola has vertex at (h,k)= (3, 9) and focus at (h,k+a)= (3, -2) Hence axis of symmetry is x=3…

Q: Write the equation for the hyperbola with foci (1,-s), (2.-s) and conjugate axis of length 6. (x-…

A: Please refer the attached image for complete solution.

Q: The equation of the sphere with center (7,-10, 1) that touches that y-axis is

A: To find the equation of the sphere we need center of the sphere  radius of the sphere.  Here given…

Q: find the ends of the latus rectum, axis of symmetry of x2+20y=0

A: Given  x2+20y=0 Find the ends of lactus rectum and axis of symmetry.

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

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Q: Consider the parabola y = -3x2+42x-150.  What is the vertex (-7,-3) (-7,3) (7,-3) (7,3)

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Q: 2. PARABOLA VERTEX = (2, FOCUS = (1,

A: Given vertex=2,1 and focus=1,1 We have to find the equation of the parabola. We can see that the…

Q: Find the vertex, directrix and graph the parabola (x–2)² =-20(y–1) 个y 9- 8- 7- 9. -5 4- 3 X -10 -9…

A: The given equation of parabola is shifted from the standard parabola.