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Equation of a Plane : Intercept Form

80. By which ...

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80. By which angle the coordinate axes must be rotated tomake equation 5x^2 +8xy +5y^2+3x +2y+5 freefrom 'xy' term?

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Q. The equation of a pair of straight lines is

{a x}^{2} + 2 h x y + b y^{2} = 0

. By what angle must the axes be rotated so that the term containing

x y

in the equation may be removed?

Q. Through what angle should the axes be rotated so that equation

a x^{2} - 2 \sqrt{3} x y + 7 y^{2} = 10 (x, y)

may be changed to

3 x^{2} + 5 y^{2} = 5 (x^{1}, y^{1})

Q. The angle of rotation of axes in order to eliminate

x y

term in the equation

x y = c^{2}

Q. The transformed equation of

3 x^{2} + 3 y^{2} + 2 x y = 2

when the coordinate axes are rotated through an angle

45^{\circ}

Q. The transformed equation of

3 x^{2} + 3 y^{2} + 2 x y = 2

when the coordinate axes are rotated through an angle of

45^{0}

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