Hyperbola- Rectangular hyperbola

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.

Asymptotes | Rectangular Hyperbola | Properties of Hyperbola and Problem Solving

The eccentricity of a rectangular hyperbola, is

Prove that the perpendicular focal chords of a rectangular hyperbola are equal.

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

The tangent at any point P on a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with centre C meets the assymptotes is bisected at the point of contact . This implies that the locus of the centre of the circle circumscribing Delta CQR in case of a rectangular hyperbola is the hyperbola itself.

COC|| Pair OF Tangent || Diameter|| Illustration|| Asymptote|| Rectangular Hyperbola (special case)