Write the equation x2 - 4xy + y2 - 3 = 0; θ = 45° in terms of a rotated x′y′-system using θ, the angle of rotation. Write the equation involving x′ and y′ in standard form.

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A: We can solve this as follows:

Q: Write the equation x2 - 4xy + y2 - 3 = 0; θ = 45°in terms of a rotated x′y′-system using θ, the…

A: Given: x2 - 4xy + y2 - 3 = 0; θ = 45°

Q: Write the equation in terms of a rotated x'y'-system using θ, the angle of rotation. Write the…

A: Given equation is We know that relation between coordinates (x,y) and (x',y') is Now,

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A: See attached file for a step by step explanation.

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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: Write the equation 23x2 + 26√3xy - 3y2 - 144 = 0; θ = 30° in terms of a rotated x′y′-system using θ,…

A: Given Data The equation is 23x²+26√3 xy-3y²-144=0. The angle is θ=30°.   Put the value in…

Q: Write the equation 13x2 - 6√3xy + 7y2 - 16 = 0; θ = 60° in terms of a rotated x′y′-system using θ,…

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

A: Given.

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Q: photo attached

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A: r=12-cosθ

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Q: Write the equation 13x2 - 6√3xy + 7y2 - 16 = 0; θ= 60° in terms of a rotated x′y′-system using θ,…

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Q: Write the equation 23x2 + 26√3xy - 3y2 - 144 = 0; θ = 45° in terms of a rotated x′y′-system using θ,…

A:

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

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Q: Please help me solve

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

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Q: Replace the Cartesian equation (x+ 4)² + (y- 2)2 = 25 with equivalent polar eauation

A: Ans :   we will convert this given cartesian equation in polar equation  by putting - x = r cosθ…

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A: We have the following facts:

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Q: b. Find a rectangular-coordinate equation by eliminating the parameter t.

A: