If the points `(x_1,y_1), (x_2,y_2) and (x_1 + x_2, y_1+y_2)` are collinear, prove that `x_1y_2 = x_2y_1`

If the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x^2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

If the points A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) are collinear, then area of triangle ABC is:

Three points P (h, k), Q(x_1, y_1) and R (x_2,y_2) lie on a line. Show that : (h-x_1)(y_2-y_1)= (k-y_1)(x_2-x_1) .

If the circle x^2+y^2=a^2 intersects the hyperbola x y=C^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then proove x_1+x_2+x_3+x_4=0 , y_1+y_2+y_3+y_4=0 , x_1x_2x_3x_4=C^4 , y_1 y_2 y_3 y_4 = C^4

If y = sin^-1x , prove that (1-x^2)y_2 - x y_1= 0

The three points (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)), (x_(3), y_(3), z_(3)) are collinear when…………

If y = x log (x/(a+bx)) , prove that x^3 y _2 = (xy_1 - y)^2

Statement 1 :If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2 : The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

The equation to the chord joining two points (x_1,y_1)a n d(x_2,y_2) on the rectangular hyperbola x y=c^2 is: x/(x_1+x_2)+y/(y_1+y_2)=1 x/(x_1-x_2)+y/(y_1-y_2)=1 x/(y_1+y_2)+y/(x_1+x_2)=1 (d) x/(y_1-y_2)+y/(x_1-x_2)=1

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2 equals