If 5x + 9 = 0 is the directrix of the hyperbola 16x² – 9y² = 144, then its corresponding focus is :

If a directrix of a hyperbola centred at the origin and passing through the point (4, –2$$\sqrt 3 $$ ) is 5x = 4$$\sqrt 5 $$ and its eccentricity is e, then :

If the line y = mx + 7$$\sqrt 3 $$ is normal to the hyperbola $${{{x^2}} \over {24}} - {{{y^2}} \over {18}} = 1$$ , then a value of m is :

If the eccentricity of the standard hyperbola passing through the point (4,6) is 2, then the equation of the tangent to the hyperbola at (4,6) is :