If `(x_1,y_1),(x_2,y_2)" and "(x_3,y_3)` are the feet of the three normals drawn from a point to the parabola `y^2=4ax`, then `(x_1-x_2)/(y_3)+(x_2-x_3)/(y_1)+(x_3-x_1)/(y_2)` is equal to

If P(x_1,y_1),Q(x_2,y_2) and R(x_3, y_3) are three points on y^2 =4ax and the normal at PQ and R meet at a point, then the value of (x_1-x_2)/(y_3)+(x_2-x_3)/(y_1)+(x_3-x_1)/(y_2)=

If P(x_(1),y_(1)),Q(x_(2),y_(2)) and R(x_(3),y_(3)) are three points on y^(2)=4ax and the normal at PQ and R meet at a point,then the value of (x_(1)-x_(2))/(y_(3))+(x_(2)-x_(3))/(y_(1))+(x_(3)-x_(1))/(y_(2))=

If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) be three points on the parabola y2=4ax, the normals at which meet in a point,then

If (x_1,y_1) , (x_2,y_2) and (x_3,y_3) are the vertices of a triangle whose area is k square units, then |{:(x_1,y_1,4),(x_2,y_2,4),(x_3,y_3,4):}|^2 is

If the tangents to the parabola y^(2)=4ax at (x_(1),y_(1)),(x_(2),y_(2)) intersect at (x_(3),y_(3)) then

Let (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) be three points on the parabola y^(2)=4ax if the normals meet in a point then

If the tangents to the parabola y^2=4ax at the points (x_1,y_1) and ( (x_2,y_2) meet at the point (x_3,y_3) then

If A(x_1, y_1), B (x_2, y_2) and C (x_3, y_3) are the vertices of a DeltaABC and (x, y) be a point on the internal bisector of angle A , then prove that : b|(x,y,1),(x_1, y_1, 1), (x_2, y_2, 1)|+c|(x, y,1), (x_1, y_1, 1), (x_3, y_3, 1)|=0 where AC = b and AB=c .

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4