Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated coordinates.) 3x2 - 2/3xy + y² + 2x + 2/3y = 0

Q: Eliminate the parameter t to find a Cartesian equation for X = 3-t = Y - 13 - 4t The Cartesian…

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Q: Eliminate the parameter t to find a Cartesian equation for: = t² X y = 2+5t The resulting equation…

A: Given x=t2 and y=2+5t

Q: Identify the equation 10x2 + 24xy + 17y2 - 9 = 0 without applying a rotation of axes.

A: We have to identify the equation  10x2 + 24xy + 17y2 - 9 = 0 without applying a rotation of axes.…

Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: The general form of quadratic equation is  Ax2+Bxy+Cy2+Dx+Ey+F=0, B≠0 The angle is  cot2θ=A-CB The…

Q: Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin. F…

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Q: Find the image of (2, -2) obtained by translating 2 units up, followed by a rotation of 90°…

A: Given point is : 2,-2 To find image of 2,-2 obtained by translating 2 units up, followed by a…

Q: Find the angle of rotation and eliminate the x-y term 4x2 - 4xy + y2 - 6x + 12 = 0

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Q: Identify the equation without applying a rotation of axes. 4x2-8xy+4y2-3x+6=0

A: Given, function is

Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: We have to determine the appropriate rotation formulas so that new equation contains no xy-term:…

Q: Eliminate the parameter t to find a Cartesian equation in the form a = f(y) for: Į z(t) l y(t) = 3t?…

A: See attached file for a step by step explanation to find the required Cartesian equation.

Q: Eliminate the parameter t to find a Cartesian equation in the form z = f(y) for: [z(t) = 3t² y(t) =…

A: We can express x in terms in terms of y as below.

Q: what is the directrix of this? (x-4)²=-24(y-2)

A: The given equation is  (x-4)2=-24(y-2)

Q: When the axes are rotated through an angle 4 π , find the transformed equation of 3x2 + 10xy + 3y2 =…

A: Axes are rotated through an angle 4π given equation is                             3x2+10xy+3y2=9…

Q: Find the polar coordinates, 0s0<2x and r20, of the following points given (a) (3, 3/3) (b) (- 2/3,…

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Q: Identify the equation 5x2 - 2xy + 5y2 - 12 = 0 without applying a rotation of axes.

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Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: Definition used -                                Ax2+Bxy+Cy2+Dx+Ey+F=0 , B≠0…

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Given equation is 16x2+8xy+8y2-13=0 Angle of rotation is ϕ to eliminate the xy term. The new…

Q: Eliminate the parameter t to find a Cartesian equation in the form x=f(y)x=f(y) for: {x(t)=−3t^2…

A: Here is the solution of the given problem.

Q: Eliminate the parameter t to find a Cartesian equation for: y = 9+ 5t The resulting equation is: Ay+…

A: From y=9+5t we get5t=y-9t=y-95

Q: Rotate the xy-axes in the plane counterclockwise through an angle θ = 60° to obtain new x' y' -axes.…

A: Given Data The angle of rotation in anticlock wise direciton is θ=60°.   (a) The expression for the…

Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term…

A: Given, 3x2 - 10xy + 3y2 - 32 = 0. It is of the form Ax2+Bxy+Cy2+Dx+Ey+F=0   On comparing we get,…

Q: A planet's orbit follows a path described by 16r + 4y? = 64. A comet follows the parabolic path y =…

A: Given: A planet's orbit follows a path described by  16x2+4y2=64 A comet follows the parabolic path…

Q: 1. Give the coordinates of the center, foci, vertices, and th equation. x2 a. y2 =1 11 - 25 x2 b. 9…

A: Given: (a)   x225-y211=1 (b)   x29-y27=-1 (c)   9x2-4y2=36

Q: 12. Applying the concept of rotation of axes, what must be the angle of rotation of the x and y axes…

A: This is a problem of vector calculus. Based on the general concept will substitute x and y value in…

Q: 33. Find the directrix. (y- 9)2 - 8 O y = -9 O y = -7 O x = -7 | x = -9

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Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: The general form is  The angle is  .

Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: If x and y axis are rotated  through an angle θ , the coordinates (x, y) of a point P relative to…

Q: Graph the image of trapezoid ABCD after a rotation 180° counterclockwise around the origin

A: Given trapezoid ABCD is in 4rth quadrant, Rotate 180∘ counter clockwise  around the originFrom the…

Q: Which of the following shows the coordinates of the given point after a rotation of 180° about the…

A: This is a simple question based on geometry which could be solved by using basic knowledge of the…

Q: 2) x2+12xy-4y2 = 30 Just draw by finding the reduced equation

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Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term…

A: Given equation is 34x2-24xy+41y2-25=0. x=x'cosθ-y'sinθ, y=x'sinθ+y'cosθ. Compare the above equation…

Q: Find the coordinates of rotation of point () by an angle /2 a. -4 b. -4 с. 1 4. d. -1 4 77 7-

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Q: Consider the following. x2 + 2 sqaureroot of 3  xy − y2 + 8 = 0 (b) Use a rotation of axes to…

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Q: 2i+3j-4k and ax1s axis. The new p

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Q: the x'y' coordinate system is rotated O degrees from the xy coordinate system. the coordinatkes of a…

A: We have (x,y) = (7,7)  Angle of rotation =45°  New coordinate = (x',y')

Q: find the rotation equation that would eliminate the xy-term 32x2 - 48xy + 18y2 - 15x - 20y = 0

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Q: Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated coordinates.) xy…

A: Given equation xy - 6x -2y = 0

Q: the Föllówing equation, identify the coordinates of the center an (x - 3)2 + (y + 2)? = 81

A: Comparing with standard form of equations of circle,

Q: identify the equation without applying a rotation of axes. 4x2-8xy+4y2-3x+6=0

A: Consider the provided equation:

Q: Transform axis inclined 30° to the original axis, the equation is x^2+2√3 xy-y^2=2a^2

A: The given equation is: x2+23xy-y2=2a2                      (1)

Q: Determine the new equation after rotated parallel to the principal axes for the equation below and…

A: Given The given equation is 2x2+4xy-y2=24. The general equation of two degrees is…

Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term…

A: Equation in general form, Ax2+Bxy+Cy2+Dx+Ey+F=0 Where, x=x'cosθ-y'sinθ and y=x'sinθ+y'cosθAnd…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: Sa(t) = 4t2 ly(t) =…

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Q: Perform a rotation of axes to eliminate the xy-term. (Use x, and Y2 for the rotated coordinates.) xy…

A: Here we use the rotational matrix.

Q: Rotate the xy-axes in the plane counterclockwise through an angle θ= 135° to obtain new x' y' -axes.…

A: Given Data The angle of rotation in anticlockwise direction is θ=135°. (a) The expression for the x’…

Q: Identify the equation without applying a rotation of axes. 2 10x² -8xy + y² +9x+3y-6=0

A: Given, 10x2-8xy+y2+9x+3y-6=0

Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term…

A: The axes of system can be rotated by some acute angle θ by keeping the origin same. Let xy-system is…

Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term.…

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Q: Eliminate the parameter t to find a Cartesian equation for 11 t -19 - 2t The Cartesian equation has…

A: A detailed solution is given below.