Sketch the graphs and find the foci; for the hyperbola, find the equations of the slant asymptotes: (x + 2)² (y – 3)² (a) 1 4 25 (x+2)² (y – 3)² (b) 1 4 25

Q: Convert the equation x2 - y2 - 2x - 4y - 4 = 0 to standard form by completing the square on x and y.…

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Q: Find the asymptotes of the hyperbola. y^2-x^2=4

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Q: The foci of the hyperbola are (0, -10) and (0, 20), and the asymptotes are y = 3/4x + 5 and y =…

A: Given, foci and asymptotes of hyperbola

Q: Find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph using…

A: given,

Q: Find the focus and directrix of the parabola given by y2 = 8x.Then graph the parabola.

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Q: Find the vertex, focus and directrix of the parabola given by y2 + 2y + 4x - 7 = 0.Then graph the…

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Q: Determine the equation of the hyperbola and its asymptotes if it has:  A)Foci F1 (7, 0) and F2 (-…

A: Let, a and b be the length of semi-major axis and semi-minor axis respectively.Given that, vertices…

Q: Graph the hyperbola whose equation is 25x2 - 16y2 - 100x - 96y - 444 = 0.Where are the foci located?…

A: Given equation of hyperbola is, 25x2-16y2-100x-96y-444=0. The standard form of equation of hyperbola…

Q: Find the center, verticies, foci, and asymptotes of the hyperbola, and sketch its graph using the…

A: Explained below

Q: Sketch the graphs of the parabolas (a) x² = 12y (b) y² + 8x = 0 and show the focus and directrix of…

A: If we have parabola in the form of  x2 = 4ay, which is a upward parabola    Then equation of…

Q: Graph the hyperbola, x2 - y2 - 2x - 2y - 1 = 0. Locate the foci and find the equations of the…

A: Given, The equation of hyperbola is  x2 - y2 - 2x - 2y - 1 = 0,

Q: Find the equation of the hyperbola having center at the origin with transverse axis on the x-axis,…

A: Given-  Hyperbola having center at the origin with transverse axis on the x-axis, a=4, and latus…

Q: Graph the hyperbola by writing the equation in standard form. Label the center, vertices and sketch…

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Q: Convert the equation 4x2 - y2 + 32x + 6y + 39 = 0 to standard form by completing the square on x and…

A: Consider the given equation as 4x2-y2+32x+6y+39=0

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

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Q: snip

A: Given: y216-x281=1 To find the asymptotoe

Q: Use the center, vertices, and asymptotes to graph the hyperbola (x + 3)2/25 -y2/16 = 1. Locate the…

A: Given: x+3225-y216=1 To Find: 1. Use the center, vertices, and asymptotes to graph the hyperbola. 2.…

Q: Graph the hyperbola x2/9 - y2 = 1. Give the location of the foci and the equations of the…

A: Given equation of hyperbola is x29-y2=1 The given hyperbola can be written as: x29-y21=1 Standard…

Q: Graph the hyperbola. Locate the foci and find the equations of the asymptotes.

A: The equation of the hyperbola is given by x216-y2=1. The standard equation of the hyperbola is of…

Q: Find the focus and directrix of the parabola given by y2 = 12x. Then graph the parabola.

A: y2=12x Now comparing with y2=4ax, we get 4a=12⇒a=3 Therefore focus is, a, 0=3, 0 & directrix is,…

Q: (y + 3)? (x - 5)² = 1 225 64

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Q: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix x…

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Q: Sketch the graph of the hyperbola, showing the vertices, foci and asymptotes. y² – 16x² = 16

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

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Q: Find the Parabola with Focus (7,-2) and Directrix x=-9

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Q: Graph the hyperbola (x - 2)2/9 - (y + 2)2/16 = 1. Give the location of the foci and the equations of…

A: Identify the values of h, k, a2 and b2 from the given equation of hyperbola. Use the formula…

Q: Find the center, foci, vertices, and eccentricity of the hyperbola                            x2/25…

A: Known fact: For the equation of the hyperbola of the form x2a2-y2b2=1, Center is 0,0 Vertices are…

Q: The foci of the hyperbola are (0, -6) and (0, 14), and the asymptotes are y = *+ 4 and y = x + 4.…

A: It is known that the equation of the hyperbola is of the form x-h2a2-y-k2b2=1 or y-k2a2-x-h2b2=1.…

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: The foci of the hyperbola are (0, -10) and (0, 20), and the asymptotes are y = 3/4x + 5 and y = -3/4…

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Q: Betty was asked to write the equation of the hyperbola with asymptotes y = +x and x-intercepts…

A: Definition used -               Equations of the asymptotes of the hyperbola are-…

Q: What is the equation of the parabola shown below, given the focus at F(1, 5) and the directrix x =…

A: Here we have to find the equation of the parabola, vertex, and equation of the axis of symmetry of…

Q: 2. Write the equation of the parabola x+ 6x+8y = 7 in standard form and identify the a) vertex, b)…

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Q: The asymptote of the hyperbola given by -=1 has the equation x2_ y? 4 2x – 3y = 0 3x – 2y = 0 Option…

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Q: Use the center, vertices, and asymptotes to graph the hyperbola. Locate the foci and find the…

A: Consider the provided hyperbola, x+229-y225=1 Find the center, vertices, and asymptotes to graph the…

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

A: The standard form of a vertical hyperbola is: (y-k)2a2-(x-h)2b2=1                        ...(i)…

Q: Graph the hyperbola y2/9 - x2 = 1. Give the location of the foci and the equations of the asymptotes

A: Equation of hyperbola  y2a2-x2b2=1           ...(1) Then foci = 0,±c, where c=a2+b2 Equation of…

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

A: Given: Foci F (0,±4) Vertices V(0,±1)

Q: Sketch the parabola with vertex at the origin and determine the focus and directrix of each. 1.…

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Write the reduced hyperbole equation, given: a) The foci ( ± 5.0), and the length L=9/2 of the rope…

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Q: Graph the hyperbola 4x2 - y2 + 8x + 6y + 11 = 0. Give the location of the foci and the equations of…

A: Given equation of hyperbola is 4x2-y2+8x+6y+11=0. Given equation can be re-written as:…

Q: The parabola has focus (0,-2) and directrix y=2.

A: equation of parabola with focus ( a , b ) and y = c  is given as below : here a = 0 b = -2  c = 2

Q: Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer…

A: According to our terms and condition i have solved starting 3 parts for remaining part please repost…

Q: Graph the hyperbola and find the indicated information. (x - 6)2 3. (y + 2)2 = 1 10 4 9. Center:…

A: Topic = Geometry

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

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

Q: Graph the hyperbola, (x - 2)2/25 - (y + 3)2/16 = 1. Locate the foci and find the equations of the…

A: Given that: The equation of the hyperbola, x-2225 - y+3216 = 1 .

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

A: Recall that the equation of hyperbola with horizontal transverse axis is given by x-h2a2-y-k2b2=1…