$\frac{y^{2}}{25}-\frac{x^{2}}{16}=1$ অধিবৃত্তের পরামিতিক সমীকরণ-

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 

If $5x+9=0$ is the directrix of the hyperbola $16{x}^{2}-9{y}^{2}=144$, then its correponding focus is:

The line $2x + y = 1$ is tangent to the hyperbola $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If this line passes through the point of intersection of the nearest directrix and the x-axis, then eccentricity of the hyperbola.

A tangent to the curve y = f(x) cuts the line y = x at a point which is at a distance of 1 unit from y - axis. The equation of the curve is