The normal at `P` to a hyperbola of eccentricity `e`, intersects its transverse and conjugate axes at `L` and `M` respectively. Show that the locus of the middle point of `LM` is a hyperbola of eccentricity `e/sqrt(e^2-1)`

The normal at P to a hyperbola of eccentricity (3)/(2sqrt(2)) intersects the transverse and conjugate axes at M and N respectively. The locus of mid-point of MN is a hyperbola, then its eccentricity.

If normal at P to a hyperbola of eccentricity 2 intersects its transverse and conjugate axes at Q and R, respectively, then prove that the locus of midpoint of QR is a hyperbola. Find the eccentricity of this hyperbola

For the hyperbola (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , the normal at point P meets the transverse axis AA' in G and the connjugate axis BB' in g and CF be perpendicular to the normal from the centre. Q. Locus of middle-point of G and g is a hyperbola of eccentricity

The normal at a variable point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 of eccentricity e meets the axes of the ellipse at Q and R .Then the locus of the midpoint of QR is a conic with eccentricity e' such that e' is independent of e(b)e'=1e'=e(d)e'=(1)/(e)

For hyperbola, If transverse axis = conjugate axis , then e =

If the eccentricity of a hyperbola is 2, then find the eccentricity of its conjugate hyperbola.