`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 line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . Then

If C is the centre of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , S, S its foci and P a point on it. Prove tha SP. S'P =CP^2-a^2+b^2

Find the equations of the tangent and normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . at the point (x_0,y_0)

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 is

The tangent to the hyperbola x^2 - y^2 = 3 are parallel to the straight line 2x + y + 8 = 0 at the following points

Show that there cannot be any common tangent to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 and its conjugate hyperbola.

If the tangent drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at any point P meets the coordinate axes at the points A and B respectively. If the rectangle OACB (O being the origin) is completed, where C lies on (x^2)/(a^2)-(y^2)/(b^2)=lambda . Then, the value of lambda is:

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ 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

For hyperbola x^2/a^2-y^2/b^2=1 , let n be the number of points on the plane through which perpendicular tangents are drawn.