5. The hyperbola is given by equation 4x2 – 9y² + 32x +54y– 53 = 0. Find the coordinates of the center, the foci, the eccentricity and the asymptotes of the hyperbola.

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices:…

A: The asymptotes of a hyperbola of the form (x-h)2a2-(y-k)2b2=1 are given by the expression…

Q: Find the general form of the equation of a hyperbola with vertices at (-2, 5) and (6, 5) and foci at…

A:

Q: What is the standard form equation of the hyperbola that has vertices (0, +4) and foci (0, +2/1…

A: Here we have vertices of the hyperbola (0,±4) and foci 0,±213

Q: Find an equation of a hyperbola in the form x2 /M - y2 /N = 1 M,N > 0 if the origin is at the…

A: Solution is given below:

Q: 3. The line segment between the vertices of a hyperbola is called the axis.

A: Given that,

Q: Do I have to use the equations for the asymptotes of a hyperbola centered at the origin, y = tr or y…

A: The equations for the asymptotes of a hyperbola centered at the origin is y = ±bax or y = ± abx.…

Q: What is the standard equation of the hyperbola if the length of its conjugate axis is 10 v5 and one…

A: To find- What is the standard equation of the hyperbola if the length of its conjugate axis is 105…

Q: 5, Rearrange the equation 4x² + 20x = 6y + 36y + 5 into the standard fo %3D hyperbola.

A: Given query is to find write the standard form of hyperbola.

Q: Find the equation of a hyperbola with center at (3,-1) if the transverse axis is horizontal, the…

A: Given Centre = (3,-1) Focal distance = 20 units Length of transverse axis = 16 units

Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: The equation for the hyperbola is 3x2-2y2+6x-8y=6. If the  y term has the minus sign,  then the…

Q: ind of an equation of a hyperbola in the form x2 / M

A: Given that:                               Centre of the hyperbola = Origin=(0, 0)Length of…

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: Rewrite the equation of the hyperbola 9x? – y? – 36x – 6y + 18 = 0 in standard form and identify - -…

A:

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

A: We have, a hyperbola satisfies the given conditions as vertical transverse axis of length 10,…

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: What is the equation of the hyperbola with asmptotes y=+-2/5x and a vertex of 0,2

A: The given problem is solved below in detail.

Q: 4. Find the standard equation of the hyperbola with the same vertices as the vertices of the ellipse…

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Q: I. Find the equation in standard form of the specified hyperbola given the following conditions. 4.)…

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Q: Find the center, foci, vertices, and eccentricity of the hyperbola                         ( y +…

A: y+32225-x-5264=1⇒y--32152-x-5282=1 Now comparing with y-k2a2-x-h2b2=1, we get k=-3, h=5, a=15 &…

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

A: Given: Foci F0,±5, conjugate axis of length 4 For given data transverse axis is on y-axis and…

Q: If PQ is a double ordinate of the hyperbola a2 1 such that AOPQ 62 is equilateral, O being the…

A: Let the hyperbola be x2a2-y2b2=1 and any double ordinate PQ be asecθ, btanθ , asecθ, -btanθ  and O…

Q: The center of a hyperbola is (-3,2). The length of the conjugate axis is 8 units, and the length of…

A:

Q: Find an equation for the hyperbola with center C(0,0), foci F(0,±9), and vertices V(0,±7).

A: Plotting the center, foci, vertices on the graph. We can say that the vertical axis is the…

Q: Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at (0,…

A:

Q: The distance from the center to a vertex of the hyperbola 4 16 is

A:

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

A:

Q: The equations of the asymptotes of a hyperbola with a parallel transverse axis (focal axis) to the y…

A: Given : equations of the asymptotes of a hyperbola with a parallel transverse axis (focal axis) to…

Q: Show that the equation x2 - 4y2 + 2x + 8y - 7 = 0 represents a hyperbola. Find its center,…

A: Given: x2-4y2+2x+8y-7=0 first we converting given equation in standard form so,…

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: 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: 3. Plot and label the center, vertices and foci of the ellipse and hyperbola and parabola. a. 4x? +…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the equation for the hyperbola with center C(0,0), foci F(0,±9), and vertices V(0,±7).

A: given center C(0,0) , foci(0,±9) and vertices (0,±7) of hyperbola  we have to find the equation for…

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices:…

A: General equation of the hyperbola:(x-h)2a2-(y-k)2b2=1             Horizontal Hyperbola…

Q: Write the equation of a circle passing through the vertices of the hyperbola 4x2-9y2=36 and having a…

A:

Q: 3. Find the standard equation for the hyperbola that has foci (0,±5) and vertices (0,±3).

A:

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

A:

Q: Find the equation of the hyperbola satisfying the given conditions. Vertices at (0,4) and (0,-4);…

A: The hyperbola satisfies the condition,vetices at 0,4 and 0,-4Foci at 0,5 and 0,-5

Q: Find the equation of the hyperbola. Foci at (3, 6) and (7, 6), and vertex at (6, 6)

A:

Q: Consider the hyperbola 3x - y´ – 24x + 4y –4 = 0. If foci are (a, b) & (c, d), then (a + b + c + d)…

A: step:-1 For a hyperbola x-h2p2 -y-k2q2=1 The co-ordinates of center is h, k The co-ordinates of foci…

Q: 4. Find the standard equation of the hyperbola with the same vertices as the vertices of the ellipse…

A:

Q: Find the standard form of the equation of the hyperbola with the given characteristics. vertices:…

A:

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Foci:  (−1,…

A:

Q: Find the equation for the hyperbola with center C (2, 4), foci F (2, 1)and F2 (2, 7), and vertices V…

A: Please see the answer in step 2

Q: Find an equation for the hyperbola that satisfies the given condition. vertices at (0, +/- 2) and…

A: Explained below

Q: The equation of the hyperbola whose foci are (0, 6) and (0,-4) and and one asym y-1= 2z is Select…

A:

Q: Find the standard form equation for a hyperbola with vertices at (0, 21) and (U, y = 74 T

A: Given :Vertices : 0, 21 and 0, -21y=74x

Q: Find the equation of the Hyperbola with Foci at (6.6). (6.30) and the vertices at (6, 12). (6, 24).…

A:

Q: Sketch the graph and find the foci of the given hyperbola 25y2-4x2=100

A: SOLUTION-

Q: 1- Sketch the hyperbola with equation 4x-3y² - 8x + 6y- 11 = 0.

A: