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Manipal MET2010MathematicsStraight Lines

If the axes be turned through an angle ⁻¹ 2 . What does the equation 4 x y-3 x^2=a^2 become?

Options

  1. AX^2-4 Y^2=a^2
  2. BX^2+4 Y^2=a^2
  3. CX^2+4 Y^2=-a^2
  4. DNone of these

Correct answer

A. X^2-4 Y^2=a^2

Step-by-step solution

Here, =2 So, = 1 5 , = 2 5 For x and y , we have x=X -Y = X-2 Y 5 and y=X +Y = 2 X+Y 5 The equation 4 x y-3 x^2=u^2 reduces to 4(X-2 Y) 5 (2 X+Y) 5 -3 ( X-2 Y 5 )^2=a^2 aligned & 4 (2 X^2-2 Y^2-3 X Y ) -3 (X^2-4 X Y+4 Y^2 )=5 a^2 aligned 5 X^2-20 Y^2=5 a^2 X^2-4 Y^2=a^2

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