The sound of a cannon firing is heard one second later at a position $B$ that at position $A$. If the speed of sound is uniform, then
the positions $A$ and $B$ are foci of a hyperbola, with cannon's position on one branch of the hyperbola
the position $A$ and $B$ are foci of an ellipse with cannon's position on the ellipse
one of the positions $A, B$ is focus of a parabola with cannon's position on the parabola
it is not possible to describe the positions of $A, B$ and the cannon with the given in formation
The locus of the centroid of the triangle formed by any point $\mathrm{P}$ on the hyperbola $16 \mathrm{x}^{2}-9 \mathrm{y}^{2}+$ $32 x+36 y-164=0$, and its foci is:
The length of the latus rectum of the hyperbola $25x^2 -16y^2 = 400$ is -
The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is $6$. The equation of the hyperbola referred to its axes as axes of co-ordinates is
Equations of a common tangent to the two hyperbolas $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}}$ $= 1 $ $\&$ $\frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}}$ $= 1 $ is :
If the latus rectum of an hyperbola be 8 and eccentricity be $3/\sqrt 5 $, then the equation of the hyperbola is