6) The diagonals of a square are along the pair of lines whose equation is 2x2-3xy-2y2=0 If (2, 1) - Maths - Straight Lines

Question

6) The diagonals of a square are along the pair of lines whose
equation is 2 x 2 - 3 x y - 2 y 2 = 0 If (2, 1) is a vertex of the
square, then the vertex of the square adjacent to it may be -
(A) (1, 4) (B) (-1, -4) (C) (-1, 2) (D) (1, -2)

Rahul Raj · Accepted Answer

dear student

2x2-3xy-2y2=02x2-4xy+xy-2y2=02x(x-2y)+y(x-2y)=0(x-2y)(2x+y)=0diagonals are line x-2y=0 and 2x+y=0point of intersection = (0,0) originso if vertex is (2,1), other vertex =(-2,-1) both on x-2y=0the other points lie on diagonal 2x+y=0points are (a,-2a) and (-a,2a)sides are perpendicularside joining (-2,-1) with points  (a,-2a) and (-a,2a)are perpendicular-2a+1a+2×2a+1-a+2=-1-4a2+1=a2-4a2=1a=±1points are (1,-2) and (-1,2)

regards

6) The diagonals of a square are along the pair of lines whose equation is 2 x 2 - 3 x y - 2 y 2 = 0 . If (2, 1) is a vertex of the square, then the vertex of the square adjacent to it may be - (A) (1, 4) (B) (-1, -4) (C) (-1, 2) (D) (1, -2)

6) The diagonals of a square are along the pair of lines whose equation is $2 x^{2} - 3 x y - 2 y^{2} = 0 .$ If (2, 1) is a vertex of the square, then the vertex of the square adjacent to it may be -
(A) (1, 4) (B) (-1, -4) (C) (-1, 2) (D) (1, -2)