Question

The point to which the axes be translated so as to remove the first degree
terms in the equation 2x^2+ 3xy - 2y^2 - 7x + y - 2 = 0 is
1) (-1, 1)
2 (1, 1)
3) (-1, -1) 4) (1, -1)​

Answer 1

The point to which the axes be translated so as to remove the first degree terms from the equation is (1, 1)

     Given equation is

        $2x^{2} +3xy-2y^{2}-7x+y-2=0$

     Here,

         a = 2, h = 3/2, b = -2, g = -7/2, f = 1/2

     The point to which the axes must be translated is given by

        $P=(\frac{hf-bg}{ab-h^{2}},\frac{gh-af}{ab-h^{2}})$

        $P=(\frac{(3/2)(1/2)-(-2)(-7/2)}{2(-2)-(3/2)^{2}},\frac{(-7/2)(3/2)-(2)(1/2)}{2(-2)-(3/2)^{2}})$

        $P=(\frac{(3/4)-(14/2)}{-4-(9/4)},\frac{(-21/4)-1}{-4-9/4})$

        $P=(\frac{3-28}{-16-9},\frac{-21-4}{-16-9})$

        $P=(\frac{-25}{-25},\frac{-25}{-25})$

        P = (1, 1)

  ∴ The correct option is 2) (1, 1)