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)`

If normal at P to a hyperbola of eccentricity e intersects its transverse and conjugate axes at L and M, respectively, then prove that the locus of midpoint of LM is a hyperbola. Find the eccentricity of this hyperbola

If normal at P to a hyperbola of eccentricity e intersects its transverse and conjugate axes at L and M, respectively, then prove that the locus of midpoint of LM is a hyperbola. Find the eccentricity of this hyperbola

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.

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.

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

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

The normal at a point P on the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2) of eccentricity e, intersects the coordinates axes at Q and R respectively. Prove that the locus of the mid-point of QR is a hyperbola of eccentricity (e )/(sqrt(e^(2)-1)) .