Question

If PN be the ordinate of a point P on the hyperbola $\frac{x^2}{(97{)}^2}-\frac{y^2}{(79{)}^2}=1$ and the tangent at P meets the transverse axis in T, O is the origin; if $ON\times OT=k$ then $\frac{\sqrt{k}+1}{14}$ is equal to

Answer 1

From properties of hyperbola
IF PN be the ordinate of a point P on the hyperbola and tangent at P meets the transverse axis in T, then $ON.OT=a^2$ , o being the origing
$\therefore k=$ $ON\times OT$=${97}^2=9409$

$\therefore \frac{\sqrt{k}+1}{14}=7$