translation of axes

An equation corresponding to a set of points with reference to a system of coordinate axes may be simplified by taking the set of points in some other suitable coordinate system, such that all geometrical properties remain unchanged. One such transformation is that in which the new ..

An equation corresponding to a set of points with reference to a system of coordinate axes may be simplified by taking the set of points in some other suitable coordinate system, such that all geometrical properties remain unchanged. One such transformation is that in which the new a..

Choose the coordinates of P (4, 5) in the translated coordinate system, when the origin is shifted to the point P (- 4, 7) without changing the direction of axes. => (- 8, - 2) or (- 8, 2) or (4, - 2) or (8, - 2)..

Choose the point to which the axes may be translated so as to remove the first degree terms in the transformed equation of 6 x 2 + 7 xy - 8 y 2 + 5 x + 4 y + 40 = 0. => (- 108 241 , 13 241 ) or (0, 0 ) or ( 108 241 , 0 ) or (241 , 0 )..

Find the discriminant of the tranformed equation of A x 2 + B x y + C y 2 + D x + E y + F = 0 when the axes are translated to ( h , k ). => B 2 - 2AC or B 2 + 4AC or B 2 - AC or B 2 - 4AC..

Choose the angle to which the axes are to be rotated so that the x' y' term in the translated equation of A x 2 + B xy + C y 2 + D x + E y + F = 0 will not be present. => θ = 1 2 Cot -1 [ A - C B ] or θ = cot - 1 [ A - C B ] or θ = 1 2 cot - 1 [ A - B C ] or &t..

Choose the angle to which the axes are to be rotated so that the x 1 y 1 term in the translated equation of A x 2 + B x y + C y 2 + D x + E y + F = 0 will not be present. => θ = 1 2 cot - 1 [ A B ] or θ = 1 2 cot - 1 [ A - C B ] or θ = 1 2 cot - 1 [ A..