If `x_1 ,y_1`, are the roots of `x^2+8x-20=0, x_2,y_2`, are the roots of `4x^2+32 x-57=0 and x_3,y_3`, are the roots of `9x^2+ 72x -112=0`, then the points, `(x_1,y_1),(x_2,y_2)and (x_3,y_3)`-

If x_1, y_1 are the roots of x^2 +8x-97=0, x_2, y_2 are the roots of 4x^2 +32x-997=0 and x_3, y_3 are the roots of 9x^2 + 72x-9997=0 . Then the point (x_1, y_1), (x_2, y_2) and (x_3, y_3)

If x_(1),y_(1), are the roots of x^(2)+8x-20=0,x_(2),y_(2), are the roots of 4x^(2)+32x-57=0 and x_(3),y_(3), are the roots of 9x^(2)+72x-112=0, then the points,(x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) -

If x_1,y_1 " are roots of " x^2+8x-20=0, x_1,y_1 " are the roots of " 4x^2+32x-57=0 and x_3,y_3 " are the roots of " 9x^2+72x-112=0 , then the points (x_1,y_1 )(x_2,y_2) and (x_3,y_3) where x_1 lt y_1 for i=1,2,3

If x_(1),y_(1) are the roots of x^(2)+8x-97=0,x_(2),y_(2) are the roots of 4x^(2)+32x-997=0 and x_(3),y_(3) are the roots of 9x^(2)+72x-9997=0. Then the point (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3))

Write the condition of collinearity of points (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

Two point B(x_(1), y_(1)) and C(x_(2), y_(2)) are such that x_(1), x_(2) are the roots of the equation x^(2)+4x+3=0 and y_(1),y_(2) are the roots of the equation y^(2)-y-6=0 . Also x_(1)lt x_(2) and y_(1)gt y_(2) . Coordinates of a third point A are (3, -5). If t is the length of the bisector of the angle BAC, then l^(2) is equal to.

y=2 is the root of y-3=2y-5x=8 is the root of (1)/(2)x+7=11

If a,B and y are the roots of x^(3)+2x+1=0 then roots of equation (x+1)^(3)+2(x^(2)-1)(x-1)-(x-1)^(3)=0 are

If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) are concurrent, prove that |(x_1,y_1,x_1y_1),(x_2,y_2,x_2y_2),(x_3,y_3,x_3y_3)|=0 .

If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (X_1, y_1), (x_2, y_2) and (x_3, y_3) are concurrent, prove that |(x_1,y_1,x_1y_1),(x_2,y_2,x_2y_2),(x_3,y_3,x_3y_3)|=0 .