`P N` is the ordinate of any point `P` on the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` and `AA '` is its transvers axis. If `Q` divides `A P` in the ratio `a^2: b^2,` then prove that `N Q` is perpendicular to `A^(prime)Pdot`

A tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its asymptotes at P and Q. If C its centre,prove that CP.CQ=a^(2)+b^(2)

Tangents at any point P is drawn to hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1 intersects asymptotes at Q and R, if O is the centre of hyperbola then

The ordinate of any point P on the hyperbola, given by 25x^(2)-16y^(2)=400 ,is produced to cut its asymptotes in the points Q and R. Prove that QP.PR=25.

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

If N is the foot of the perpendicular drawn from any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a>b) to its major axis AA' then (PN^(2))/(AN A'N) =

P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transvers axis at Tdot If O is the center of the hyperbola, then find the value of O TxO Ndot

P is a point on the hyperbola (x^(2))/(y^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T . If O is the centre of the hyperbola, then OT . ON is equal to

A tangent is drawn at any point on the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 . If this tengent is intersected by the tangents at the vertices at points P and Q then show that S, S' , P and Q are concyclic points where S and S' are the foci of the hyperbola .