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
If the line $y\, = \,mx\, + \,7\sqrt 3 $ is normal to the hyperbola $\frac{{{x^2}}}{{24}} - \frac{{{y^2}}}{{18}} = 1,$ then a value of $m$ is
Let $P(6,3)$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If the normal at the point $P$ intersects the $x$-axis at $(9,0)$, then the eccentricity of the hyperbola is
A square $ABCD$ has all its vertices on the curve $x ^{2} y ^{2}=1$. The midpoints of its sides also lie on the same curve. Then, the square of area of $ABCD$ is
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $49 y^{2}-16 x^{2}=784$
Let the focal chord of the parabola $P: y^{2}=4 x$ along the line $L: y=m x+c, m>0$ meet the parabola at the points $M$ and $N$. Let the line $L$ be a tangent to the hyperbola $H : x ^{2}- y ^{2}=4$. If $O$ is the vertex of $P$ and $F$ is the focus of $H$ on the positive $x$-axis, then the area of the quadrilateral $OMFN$ is.