Show that the midpoints of focal chords of a hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` lie on another similar hyperbola.

The midpoint of the chord 4x-3y=5 of the hyperbola 2x^(2)-3y^(2)=12 is

The locus of the point of intersection of the tangents at the end-points of normal chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is

Find the length of chord x-3y-3=0 of hyperbola (x^(2))/(9)-(y^(2))/(4)=1

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

Locus of mid-points of chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 ,such angle between tangents at the end of the chords is 90^(@) is:

Show that the equation of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (a sqrt(2),b) is ax+b sqrt(2)y=(a^(2)+b^(2))sqrt(2)

The locus of the midpoint of the chords of the hyperbola (x^(2))/(25)-(y^(2))/(36)=1 which passes through the point (2, 4) is a hyperbola, whose transverse axis length (in units) is equal to