If hyperbola `x^(2)-y^(2)=a^(2)` and `xy=c^(2)` are of same size,then:

If e_(1)ande_(2) be the eccentricities of the hyperbola xy=c^(2)andx^(2)-y^(2)=c^(2) respectively then :

From a point P, tangents are drawn to the hyperbola 2xy = a^(2) . If the chord of contact of these tangents touches the rectangular hyperbola x^(2) - y^(2) = a^(2) , prove that the locus of P is the conjugate hyperbola of the second hyperbola.

Eccentricity of the hyperbola x^(2) - y^(2) = a^(2) is :

The angle between the hyperbola xy = c^(2) " and " x^(2) - y^(2) = a^(2) is

If e and e_(1) , are the eccentricities of the hyperbolas xy=c^(2) and x^(2)-y^(2)=c^(2) , then e^(2)+e_(1)^(2) is equal to

If the hyperbolas,x^(2)+3xy+2y^(2)+2=0 and x^(2)+3xy+2y^(2)+2x+3y+c=0 are conjugate of each other,then the value of c' is equal to

If e_(1) and e_(2) are the eccentricites of hyperbola xy=c^(2) and x^(2)-y^(2)=c^(2) , then e_(1)^(2)+e_(2)^(2)=

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in four points P(x_(1),y_(1)),Q(x_(2),y^(2)),R(x^(3),y^(3)),S(x^(4),y^(4)) then