If any line perpendicular to the transverse axis cuts the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` and the conjugate hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=-1` at points `Pa n dQ` , respectively, then prove that normal at `Pa n dQ` meet on the x-axis.

If any line perpendicular to the transverse axis cuts the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and the conjugate hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 at points P and Q, respectively,then prove that normal at P and Q meet on the x-axis.

The tangent at the vertex of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its conjugate hyperbola at the point whose coordinates are

The pole of the line lx+my+n=0 with respect to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is

The pole of the line lx+my+n=0 with respect to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is

If the ratio of transverse and conjugate axis of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passing through the point (1,1) is (1)/(3), then its equation is

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

If the tangents drawn from a point on the hyperbola x^(2)-y^(2)=a^(2)-b^(2) to ellipse (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle alpha and beta with the transverse axis of the hyperbola, then