Auxiliary Circle & Eccentricity Angle|| Chord Joining p(α),( β)|| Rectangular hyperbola

Auxiliary Circle and eccentric angle

The eccentricity of a rectangular hyperbola, is

Hyperbola- Auxiliary circle || Eccentric angle || Position OF point || Equation OF tangent || Equation OF chord at A(α),B(β)

Find all values for xy=c^(2) (assymptotes; transverse axis; conjugate axis; vertex; focii length of latus rectum; Equation of auxilliary circle; equation of directrix circle and hyperbola and rectangular hyperbola intersects at right angle.

The chord of contact of a point P w.r.t a hyperbola and its auxiliary circle are at right angle.Then the point P lies on conjugate hyperbola one of the directrix one of the asymptotes (d) none of these

The eccentricity of rectangular hyperbola is sqrt(2)

Prove that the eccentricity of a rectangular hyperbola is equal to sqrt2 .

The tangent at a point P(a cos phi,b sin phi) of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets its auxiliary circle at two points,the chord joining which subtends a right angle at the center.Find the eccentricity of the ellipse.