The vertices of a hyperbola are at $(0, 0)$ and $(10, 0)$ and one of its foci is at $(18, 0)$. The equation of the hyperbola is
$\frac{{{x^2}}}{{25}} - \frac{{{y^2}}}{{144}} = 1$
$\frac{{{{(x - 5)}^2}}}{{25}} - \frac{{{y^2}}}{{144}} = 1$
$\frac{{{x^2}}}{{25}} - \frac{{{{(y - 5)}^2}}}{{144}} = 1$
$\frac{{{{(x - 5)}^2}}}{{25}} - \frac{{{{(y - 5)}^2}}}{{144}} = 1$
If $(a -2)x^2 + ay^2 = 4$ represents rectangular hyperbola, then $a$ equals :-
For the Hyperbola ${x^2}{\sec ^2}\theta - {y^2}cose{c^2}\theta = 1$ which of the following remains constant when $\theta $ varies $= ?$
The foci of the hyperbola $2{x^2} - 3{y^2} = 5$, is
The graph of the conic $ x^2 - (y - 1)^2 = 1$ has one tangent line with positive slope that passes through the origin. the point of tangency being $(a, b). $ Then Eccentricity of the conic is
The locus of the point of intersection of the lines $bxt - ayt = ab$ and $bx + ay = abt$ is