If `x_1`, `x_2`, `y_1`, `y_2` `in R` if `0

For x_(1), x_(2), y_(1), y_(2) in R if 0 lt x_(1)lt x_(2)lt y_(1) = y_(2) and z_(1) = x_(1) + i y_(1), z_(2) = x_(2)+ iy_(2) and z_(3) = (z_(1) + z_(2))//2, then z_(1) , z_(2) , z_(3) satisfy :

For x_(1), x_(2), y_(1), y_(2) in R if 0 lt x_(1)lt x_(2)lt y_(1) = y_(2) and z_(1) = x_(1) + i y_(1), z_(2) = x_(2)+ iy_(2) and z_(3) = (z_(1) + z_(2))//2, then z_(1) , z_(2) , z_(3) satisfy :

For x_1,x_2, y_1, y_2 in R , if 0

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 the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0

Find the 2xx2 mtrix X if [[x_1,x_2], [y_1,y_2]]-[[2,0],[0,2]]=[[3,5],[1,2]] determine x_1,x_2,y_1,y_2 .

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

The total number of matrices A = [{:(0, 2y, 1), (2x, y, -1), (2x, -y, 1):}] (x, y in R, x ne y) for which A^(T)A = 3I_(3) is

If the points P(h , k),\ Q(x_1, y_1)a n d\ 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)dot

Three points P(h, k), Q(dotx_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)