If a rectangular hyperbola circumscribes a triangle, show that the curve passes through the orthocentre of the triangle. Find the distances from `A(4, 2)` to the points in which the line `3x-5y=2` meets the hyperbola `xy=24`.

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

The radius of the circle passing through the vertices of the triangle formed by the lines x + y = 2, 3x - 4y = 6, x - y = 0

The normal to the rectangular hyperbola xy = 4 at the point t_1 meets the curve again at the point t_2 Then

Orthocentre of the triangle formed by the lines xy-3x-5y+15=0 and 3x+5y=15 is

Normal at 3 points P, Q, and R on a rectangular hyperbola intersect at a point on a curve the centroid of triangle PQR

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

The distance of the origin from the normal drawn at the point (1,-1) on the hyperbola 4x^2-3y^2=1 is

The vertices of triangleABC lie on a rectangular hyperbola such that the orhtocentre of the triangle is (2,3) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). Q. The equation of the rectangular hyperbola is

The orthocentre of the triangle formed by the lines 2x^(2)+3xy-2y^(2)-9x+7y-5=0 with 4x+5y-3=0 is

The vertices of triangleABC lie on a rectangular hyperbola such that the orhtocentre of the triangle is (2, 3) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). Q. The number of real tangents that can be drawn from the point (1, 1) to the rectangular hyperbola is