A circle cuts the rectangular hyperbola `xy=1` in the points `(x_(r),y_(r)), r=1,2,3,4`.
Prove that `x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=1`

If the normals at four points P (x_i y_i), i = 1, 2, 3, 4 on the rectangular hyperbola xy = c^2 , meet at the point Q(h, k), then prove that x_1 + x_2 + x_3 + x_4 =h

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

An equilateral triangle has each of its sides of length 4 cm. If (x_(r),y_(r)) (r=1,2,3) are its vertices the value of |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|^2

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

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 A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC 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 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

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

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