If `P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4)` are four concyclic points on the rectangular hyperbola ) and `xy = c^2` , then coordinates of the orthocentre ofthe triangle `PQR` is

If four points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) and (x_(4),y_(4)) taken in order in a parallelogram, then:

If the normals at (x_(i),y_(i)) i=1,2,3,4 to the rectangular hyperbola xy=2 meet at the point (3,4) then

From the point (x_1, y_1) and (x_2, y_2) , tangents are drawn to the rectangular hyperbola xy=c^(2) . If the conic passing through the two given points and the four points of contact is a circle, then show that x_1x_2=y_1y_2 and x_1y_2+x_2y_1=4c^(2) .

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). x y=4 (b) x y=1/4 x y=1 (d) none of these

If the equations of three sides of a triangle are x+y=1, 3x + 5y = 2 and x - y = 0 then the orthocentre of the triangle lies on the line/lines

If the normal to the rectangular hyperbola x^(2) - y^(2) = 4 at a point P meets the coordinates axes in Q and R and O is the centre of the hyperbola , then

The points A (x_(1),y_(1)), B (x_(2),y_(2)) and C (x_(3),y_(3)) are the vertices of triangle ABC. (i) The median from A Meets Bc at D. Find the coordinates of the points D. (ii) Find the coordinates of the point P on Ad such that AP : PD = 2 : 1 . (iii) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE=2 :1 and CR : RF =2 : 1 . What are the coordinates of the centroid of the triangle ABC?

A circle with centre (3alpha, 3beta) and of variable radius cuts the rectangular hyperbola x^(2)-y^(2)=9a^(2) at the points P, Q, S, R . Prove that the locus of the centroid of triangle PQR is (x-2alpha)^(2)-(y-2beta)^(2)=a^(2) .

The orthocentre of the triangle formed by the lines x=2,y=3 and 3x+2y=6 is at the point

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