If ` [[x-y,2x-x_1],[2x-y,3x+y_1]], =[[-1,5],[0,13]]` and coordinats of points P and Q be (x,y) and `(x_1,y_1)` respectively then P,Q=?

If [[x-y, 2x+z],[2x-y,3z+omega]] =[[-1,5],[0,13]] find x+y+z+omega

[[ x-y,2x+z] , [ 2x-y,3z+w ]] = [[ -1, 5 ] , [ 0, 13 ]], then ,x,y,z,w is?

If the coordinates of any two points Q_1 and Q_2 are (x_1,y_1) and (x_2,y_2) , respectively, then prove that OQ_1xxOQ_2cos(angleQ_1OQ_2)=x_1x-2+y-1y_2 , whose O is the origin.

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

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

Let each of the circles, S_(1)=x^(2)+y^(2)+4y-1=0 , S_(2)=x^(2)+y^(2)+6x+y+8=0 , S_(3)=x^(2)+y^(2)-4x-4y-37=0 touches the other two. Let P_(1), P_(2), P_(3) be the points of contact of S_(1) and S_(2), S_(2) and S_(3), S_(3) and S_(1) respectively and C_(1), C_(2), C_(3) be the centres of S_(1), S_(2), S_(3) respectively. Q. The co-ordinates of P_(1) are :

If O is the origin and P(x_(1),y_(1)), Q(x_(2),y_(2)) are two points then OPxOQ sin angle POQ=

If the distances of P(x, y) from A(5,1) and B(-1, 5) are equal, then prove that 3x=2y.

Let C_1 and C_2 be respectively, the parabolas x^2=y-1 and y^2=x-1 Let P be any point on C_1 and Q be any point on C_2 . Let P_1 and Q_1 be the refelections of P and Q, respectively with respect to the line y=x. If the point p(pi,pi^2+1) and Q(mu^2+1,mu) then P_1 and Q_1 are

Let C_1 and C_2 be respectively, the parabolas x^2=y-1 and y^2=x-1 Let P be any point on C_1 and Q be any point on C_2 . Let P_1 and Q_1 be the refelections of P and Q, respectively with respect to the line y=x. Arithemetic mean of PP_1 and Q Q_1 is always less than