Prove that the area of the triangle cut off from the coordinate axes by a tangent to a hyperbola is constant.

Find the value of |a| for which the area of triangle included between the coordinate axes and any tangent to the curve x y^a = lamda ^(a+1) is constant (where lamda is constant.)

Find the value of |a| for which the area of triangle included between the coordinate axes and any tangent to the curve x ^(a) y = lamda ^(a) is constant (where lamda is constnat.),

If the area of the triangle included between the axes and any tangent to the curve x^n y=a^n is constant, then find the value of ndot

If the area of the triangle included between the axes and any tangent to the curve x^n y=a^n is constant, then find the value of ndot

Prove that the area of a triangle is invariant under the translation of the axes.

In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).

In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

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