For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or the y-axis. y? 1 15 20

Q: Show that the equation represents a sphere, and find its center and radius: x? + y? + z2 – 2x – 4y +…

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Q: Q 03: find the orthogonal trajectory of family of parabolas represented by the equation y? = 4ax…

A: Given y2 = 4ax2y dydx = 4adydx = 4a2ya = 2yy'4= yy'2y2 = 2xy dydx

Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

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Q: What are the foci of the ellipse? 49 42 O (2+ v7, 1) o (2+ 7, -1) o (tyī, 1) o (12/7, - 1)

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Q: y? What is the length of the transverse axis of the hyperbola 25 |3D 64 O 8 units 16 units O 5 units…

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Q: 5. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? O y = (# – 1)2 +…

A: y= (1/4) *(x-1)^2 +3

Q: What is the equation of a parabola with focus at (2,6) and directrixx = 8? %3D O y - 12y + 12z – 24…

A: Equating distance from directrix to distance from focus gives equation of parabola.

Q: In which direction do the following parabolas open?a. y2 = -4x        b. x2 = 4y

A: Part(a) Given parabola  The graph of the given parabola is

Q: - For the hyperbola - = 1, the value of a is the 4 value of b is ,and the transverse axis is the…

A: The general equation of the hyperbola is x2a2-y2b2=1.Here a is the distance from the vertex to the…

Q: What is the directrix of the parabola? (x + 3)² = 8 (y – 1) y = 3 O y = 2 O y = 1 O y = -1

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Q: he area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: We have to find percent change in the area after increasing major axis and minor axis.

Q: Which point or points on the ellipse x? +4y? = 4 are furthest away from the point (0, 1)?

A: The Equation of the given ellipse is, x2+4y2=4 Let the furthest away point on the ellipse, from the…

Q: By differentiating implicitly, find the slope of the hyperboloid x² + y? – 22 =1 in the x-direction…

A: Given that: x2+y2-z2=1

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A: Given: To Find: Which of the following option is correct:a. x-h2a2-y-k2b2=1b. y-k2a2-x-h2b2=1

Q: What is the shape of the vertical cross section of this solid figure that does not pass through the…

A: 2)circle

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

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Q: Which of the following correctly depicts the sphere given by the equation: x2 + (y - 2)2 + (z - 2)2…

A: Given: x2 + (y - 2)2 + (z - 2)2 = 4

Q: What is the center of the hyperbola? (y+3)? 9. (x-2)2 =D1 2 Enter your answer by filling in the…

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Q: find the equation of a sphere with the line segment AB as one of its diameters, where A(-3, 2, 1)…

A: We have to find the equation of a sphere with the line segment AB as one of its diameters, where…

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Given directrix: x=0 and focus (-4,5)The vertex will be the mid point of them Mid point of x=0 and…

Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

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Q: Q1. Find the equation of sphere whose center is at (4,-1, 7) and radius is 5.

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Q: What is the directrix of the parabola? (z+3) =8 (y-1) O y= 3 O y=2 O y= 1 o y=-1

A: If General equation of parabola :  y = a ( x - h ) 2 + k  Then directrix y = k - ( 1/4a )

Q: Use the Distance Formula to write an equation of the parabola with focus F(0. 9) an y%3D

A: Topic- equation of parabola

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

A: Given: Corners of the reference rectangle: (8, 7), (−6, 7), (8, −3), (−6, −3); Horizontal transverse…

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: Find the point P on the parabola y = x? closest to the point (57, 0). (x, V) = ( y y =x 57

A: Let x, x2 be the point on the parabola y=x2 closest to the point 57, 0. Now the distance between x,…

Q: Use the figure to complete the sentence below. Y Transverse ais If the center of the hyperbola is…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: Find the equation of the sphere

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Q: For the sphere with equation (x - 1) + (y + 2) + (z + 4) = 36, find a) the center. b) the length of…

A: The given sphere equation is x-12+y+22+z+42=36.

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 3? a = b…

A: Slope of the tangent is obtained by dy/dx

Q: 4. Label the focus, directrix, and vertex on the graphs given for the parabolas in Exercises 2 and…

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Q: bétween the spheres and 2- + Y 4 if the dênsity at any point is equal to the square of its distance…

A: Given: The solid lies above the cone 3z=x2+y2 and between the sphere x2+y2+z2=1 and  x2+y2+z2=4  The…

Q: Which equation represents a parabola with focus (2, 6) and directrix y = 2? A. y+4=(x-2)² 10 B.…

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Q: Consider the parabola - 2.x? + 20x – 4y – 62 = 0 O What is the vertex of this parabola? (r, y) What…

A: The given parabola is:…

Q: Find ? for which the line tangent to the parabola ? = 4? − ?^2 is horizontal

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Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

A: The general equation of the horizontal transverse axis hyperbola is given by,

Q: c) Find the center and radius of the sphere whose equation is x2 + y? + z? + 10x + 4y + 2z – 19 = 0

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Q: Evaluate y ds, where C is the parabola r (3t2, 3t), for 0 <t< 1. %3D

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

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Q: For Exercise, determine the standard form of the parabola subject to the given conditions. Focus:…

A: Given:Focus: (0, −3);  Directrix: y = −6

Q: What is the distance from the y-axis to the focus of the hyperbola whose equation is (y – 1)? –…

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Q: Find the equation of the circle that contains all corners of the auxiliary rect- angle of the…

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Q: hat is the shape of the vertical cross section of this solid figure that passes through the vertex?

A: We have to identify the shape of the cross-section.

Q: Find equations for two lines through the origin that are tangent to the ellipse x? – 4x + y? + 3 =…

A: Solve for the equation

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

A: From the given statement, the corners of the reference rectangle are  (7,6), (-1,6), (7,0), (-1,0)…

Q: 3. What is the radius of the circle passing through the vertex and endpoints of the latus rectum of…

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Q: For Exercise, determine the standard form of the parabola subject to the given conditions. Vertex:…

A: To determine the standard form of the parabola.