2. Find the equation of the hyperbola whose asymptotes are perpendicular to the lines 5x – 4y +9 = 0 and –8x + 7y – 2 = 0 , whose center is at (1,–2) and which passes through the point (0,–1).

Q: Which of the following is the equation representing one of the asymptotes of the hyperbola 4x- 25y =…

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Q: 1. Suppose that the equation Ax + Cy + Dx + Ey + F = 0 represents a conic section (nondegenerative…

A: Fill in the blanks

Q: Identify and sketch the graph of the conic section.x2 + y2 + 4x − 2y − 11 = 0

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

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Q: A. Reduce each of the following equations of hyperbolas in standard form. 1.) 4x² – y? + 2y - 5 = 0…

A: We have to obtain the standard form of the given equations.

Q: (x – 1)2 (y + 1)2 1? Which of the following lines is an asymptote of the hyperbola 9. O 3x + 2y - 1…

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Q: Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1. f(x) 4 O (x) =…

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Q: Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11. O (x)= (X +…

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Q: Show that the image of the hyperbola x² - y² = 1 is the transiscate p² = cos24.

A: Introduction: An hyperbola is another significant conic section. It has Cartesian as well as polar…

Q: 3. Where do the asymptotes intersect for the hyperbola y = ( 2x +3 ) / ( 8x +5 ) O ( 3/8 , 2/5 ) O…

A: Given : Hyperbola y =2x + 38x + 5   To find the asymptotes.

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: The hyperbola in Position I opening up opening down in Position II y² x² 4 16 1 is

A: Topic :- geometry

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

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

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Q: Which of the following lines is an asymptote of the hyperbola (2- 1) (y+1)2 = 1? 4 9. O 2x +3y-1 = 0…

A: We will find the asymptotes of the hyperbola.Below find the solution in the image.

Q: Identify the graph of the given nondegenerate conic sections: y2 - 12x - 4y + 52 = 0

A: A nondegenerate conic section of the form         Ax2+Cy2+Dx+Ey+F=0 a)If A=C then circle b)If AC=0…

Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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Q: Identify the graph of each of the following nondegenerate conic sections: a. 4x2 - 25y2 - 24x + 250y…

A: The graph of the non-degenerate conic section: 4x2 - 25y2 - 24x + 250y - 489 = 0 ; is as follows:

Q: -9 81 -2 9 8 7 6 Which best represents the equation of the graphed conic section?

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Q: The equatione of aoymptoteo ofthe hyperbola 9 (y-9)2-4(x-7)2= 36 are Select one: O 2(y-9)=+3 (x-7) O…

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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: 2 Find the transformed equation of the hyperbola xy = 4 when rotated 45. (x')² - (y')² = 8…

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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: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: The equations of asymptotes of the hyperbola 36 (y -7)2- 25 (x-9)²=900 are Select one: O 5 (y - 7) =…

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Q: 4) Consider the images of the hyperbolas r - y = ±c? under the mapping f(2) = 22, where c > 0. Show…

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Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

Q: 1- Sketch the following conic sections: Aa-. y-4y+8- 4x2 -0 b- y2 -4y-4x2 = 8 c- 3(y- s)2 - 7(x +…

A: Since, you have asked multiple questions , we will solve the first question for you. Also, the first…

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

A: Suppose that the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 represents a conic section…

Q: Find the point on the ellipse x2 + 6y² + 3xy = 40 with the largest x-coordinate (Figure ). -8 FIGURE…

A: Given: x2+6y2+3xy=40

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. Which Is the corresponding equation of a hyperbola with co-vertices at (0, -6) and (0, 6) and a…

A: Given, The co-vertices of the hyperbola are 0, -6 and 0, 6  and transverse axis is 20 units long.…

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: 9. Find an equation of the hyperbola whose transverse axis is horizontal, with center at (2, –2) and…

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Q: Find an equation for the conic whose graph is shown. y F (6, 0)

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Q: The equation of the hyperbola whose foci are (V5, 1) and (-V5, 1) and one asymptote y –1= 2x is…

A: Given: Foci=(5,1),(-5,1) Asymptote=y-1=2x

Q: Compute the angle between the asymptotes of the hyperbola 5y² - 4x² + 40y + 60 = 0 Select one: O a.…

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Q: Find the asymptotes of the hyperbola. (x- 2)? (y-42 = 1 16 %3D 9. 4 4 O A. y=(x-2) and y= -(x-2) 3 3…

A: Given:        x-229-y-4216=1

Q: The parabola y + 2y + 8x –7=0 has vertex at O (-1, –1) o (-1,1) о (1,-1) о (1,1)

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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: Identify the type of conic section from the equation: y^2 - 4y - x^2 6x =12

A: We have been given the equation  y2-4y-x2+6x=12

Q: Sketch the conic sections. Indicate the foci, and show your work: A) 4x2+3y2+8x-6y=5 B)…

A: A)Given equation is,

Q: Identify and sketch the graph of the conic section.y2 − 6y − 4x + 21 = 0

A: Consider the given equation whose type of conic section is to identify:

Q: And identify what conic section  -x^2+4y^2-8y-96=0

A: Given -x2+4y2-8y-96=0

Q: The conic section whose equation is x2 - 3y2 - 8x + 12y + 16 = 0, is ______. centered on the origin…

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Q: Find the equation of the Hyperbola whose Foci are at (2,1) and ( 10,1),and the length of its…

A: Given: Foci ≡ 2,1 and 10,1, Length of the Transverse axis = 4

Q: The hyperbola (y + 2)2 (a+ 7)2 = 1 64 81 has asymptotes which are the two lines y=土 8/9 ( x+7 2.

A: First write the standard hyperbola equation then compair and find all the values then write the…