A tangent drawn to hyperbola $\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$ at $P\left(\dfrac{\pi}{6}\right)$ forms a triangle of area $3a^{2}$ square units, with coordinate axes. Its eccentricity is equal to 

যদি $5 x+9=0$ রেখাটি$16 x^{2}-9 y^{2}=144$, অধিবৃত্তের একটি নিয়ামক রেখা হয় তবে তার অনূরুপ কেন্দ্র -

$\frac{x^{2}}{5}-\frac{y^{2}}{4}=1$ অধিবৃত্তের নিয়ামকের সমীকরণ কোনটি?

If $\frac { (3x-4y-{ 1) }^{ 2 } }{ 100 } -\frac { (4x+3y-{ 1) }^{ 2 } }{ 225 } =1,$ then length latusrectum of hyperbola is-

The hyperbola $\dfrac { { x }^{ 2 } }{ { a }^{ 2 } } -\dfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$ passes through the point of intersection of the lines $x-3\sqrt { 5 } y=0$ and $\sqrt { 5 } x-2y=13$ and the length of its flatus rectum is 4/3 units. The coordinates of its focus are-