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

For the standard hyperbola x^2/a^2-y^2/b^2=1 ,

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

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)) .

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: