The tangent at the vertex of the hyperbola `x^2/a^2-y^2/b^2=1` meets its conjugate hyperbola at the point whose coordinates are

The conjugate axis of the hyperbola x^2/a^2+y^2/b^2=1 meets the hyperbola at two points which are at distance 2b from each other.

If e and e\' are the eccentricities of the hyperbola x^2/a^2 - y^2/b^2 = 1 and its conjugate hyperbola, prove that 1/e^2 + 1+e\'^2 = 1

If e and e' are the eccentricities of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 and its conjugate hyperbola,the value of 1/e^(2)+1/e^prime2 is

The asymptote of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 form with any tangent to the hyperbola a triangle whose area is a^2 tanlambda in magnitude, then its eccentricity is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot