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 the middle point of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 Which passes through a fixed point (alpha,beta) is hyperbola whose centre is (A) (alpha,beta) (B) (2 alpha,2 beta) (C) ((alpha)/(2),(beta)/(2)) (D) none

The locus of the middle points of the chords of hyperbola (x^(2))/(9) - (y^(2))/(4) =1 , which pass through the fixed point (1, 2) is a hyperbola whose eccentricity is

The locus of the poles of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which subtend a right angle at its centre is

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

Find the locus of the middle points of the normals chords of the rectangular hyperbola x^(2)-y^(2)=a^(2)

Find the locus of the mid-points of the chords of the hyperbola x^(2)-y^(2)=1 which touch the parabola y^(2)=4x

The locus of midpoint of the chords of hyperbola (x^(2))/(25)-(y^(2))/(36)=1 which passes through the point (2,4) is a conic whose eccentricity is

locus of the middle point of the chords of the circle x^(2)+y^(2)+2gx+2fy+c=0 which passed through a fixed point (a,b)

The locus of the middle points of the portions of the tangents of the hyperbola. (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 included between the axes is