Perform a rotation of axes to eliminate the xy-term. (Use x, and Y2 for the rotated coordinates.) xy - 8x - 4y = 0

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

A:

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

A:

Q: b) Find the counter-clockwise angle of rotation of axes to remove the xy term in the equation 12x² +…

A:

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

A:

Q: Watch help Video What is the image of the point (-8,0) after a rotation of 270° counterclockwise…

A: Given query is to find the coordinates of the point after 270° counter clockwise rotation.

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 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: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for ( a(t)…

A:

Q: Write the appropriate rotation formulas so that in a rotated system the equation 6x2 - 6xy + 14y2 -…

A:

Q: 2 -10 -8 -6 -4 -2 2 8 -2 C hp -> 4. 6, Co

A: topic - rotation of a rectangle around origin

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

A:

Q: b) Find the counter-clockwise angle of rotation of axes to remove the xy term in the equation 12x² +…

A: Given.

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: 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: Eliminate the parameter t to find a Cartesian equation in the form z = f(y) for: S r(t) = 2t2 l y(t)…

A:

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: 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: 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: Determine the coordinate of a 3D point (100.0, 29.0, -79.5) after rotating 60° across Y-axis, given…

A: Given:                       point: A100.0,29.0,-79.5                Rotation: θ = 60° across…

Q: Eliminate the parameter t to find a Cartesian equation for: x = t2 y = 7 + 5t The resulting equation…

A:

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: Rewrite the equation in a rotated x′y′​-system without an x′y′​-term. Use the appropriate rotation…

A: Consider the given equationx2+xy+y2-19=0.the general form of cartesian conic equation…

Q: Eliminate the parameter t to find a Cartesian equation in the form Y f(x) for: S 2(t) l y(t) - 2 +…

A:

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: Q.10 If a 2i-3j + 4k and b-2j +4k Find the component or projection of a along b.

A: Component or projection of a→ along b→ is  a →. b→b→.

Q: 5T Find the rectangular coordinates for the point (-1,).

A:

Q: Find a parametric representation of the solution set of the linear equation. (Enter your answer as a…

A:

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

A:

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

A:

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: S21: The Cartesian coordinates of

A:

Q: [-1 0 Use 3 to reflect over the y-axis. Identify the transformed -4 1 parallelogram.

A:

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: when the axes are rotated through an angle x/4,find the transformed equation of 3x2+10xy+3y2=9

A:

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: HiwiL showthat_Vi= 3i+6j_and Vz =-i-2j_have opfosite directionr.

A:

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.…

A:

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.