Curve having eccentricity `sqrt2` is a rectangular hyperbola.

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

The value of e for rectangular Hyperbola is …….

e_(1) and e_(2) are eccentricities of hyperbola and conjugate hyperbola respectively then prove that (1)/(e_(1)^(2))+(1)/(e_(2)^(2))=1.

Figure shows the variations of the internal energy U With density rho one mole an ideal monatomic gas for thermodynamic cycle ABCA . Here process AB is a part of rectangular hyperbola,-

If the equation (a-3)x^2+9y^2=4 represents the rectangular hyperbola then a = ........... .

Find the corrdinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas : (i) (x^(2))/(9)-(y^(2))/(16)=1 (ii) y^(2)-16x^(2)=16

If the distance between the foci of a hyperbola is 16 and its eccentricity is sqrt(2) , then obtain the equation of the hyperbola.

…….of the following is not the eccentricity of hyperbola.

Prove that sqrt2+sqrt2 is irrational .

Show that sqrt2 is irrational.