The transformed equation of 4xy - 3x2 =10 when the axes are rotated through an angle whose tangent is ‘2’ is

tanθ=2, Find sinθ =25and cosθ=15 x=X5-2Y5,y=2X5+Y5subtute in equation

The transformed equation of 4xy - 3x2 =10 when the axes are rotated through an angle whose tangent is ‘2’ is

tanθ=2, Find sinθ =25and cosθ=15 x=X5-2Y5,y=2X5+Y5subtute in equation

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The transformed equation of 4xy - 3x² =10 when the axes are rotated through an angle whose tangent is ‘2’ is

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$X^{2} - 4 Y^{2} = 10$

$4 X^{2} - Y^{2} = 10$

$X Y - 10 = 0$

$2 X^{2} - Y^{2} + 10 = 0$

answer is A.

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Detailed Solution

$\tan θ = 2$ , Find $\sin θ$ = $\frac{2}{\sqrt{5}}$ and $\cos θ = \frac{1}{\sqrt{5}} x = \frac{X}{\sqrt{5}} - \frac{2 Y}{\sqrt{5}}, y = \frac{2 X}{\sqrt{5}} + \frac{Y}{\sqrt{5}}$

subtute in equation

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The transformed equation of 4xy - 3x2 =10 when the axes are rotated through an angle whose tangent is ‘2’ is

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The transformed equation of 4xy - 3x² =10 when the axes are rotated through an angle whose tangent is ‘2’ is