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 det[[x_(2),y_(2),x_(2)y_(2)x_(3),y_(3),x_(3)y_(3)]]=0

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

Prove that the points : (x_1,y_1),(x_2,y_2),(x_3,y_3) are collinear if [[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]] =0

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 (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 (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 (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 (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 (x_1,y_1),(x_2,y_2)and(x_3,y_3) are collinear, then the rank of the matrix {:[(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)]:} will always be less than

If the points (x_1,y_1),(x_2,y_2)and(x_3,y_3) are collinear, then the rank of the matrix {:[(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)]:} will always be less than