If e₁ and e₂ are the eccentricities of the ellipse, $${{{x^2}} \over {18}} + {{{y^2}} \over 4} = 1$$ and the hyperbola, $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ respectively and (e₁, e₂) is a point on the ellipse, 15x² + 3y² = k, then k is equal to :

If a hyperbola passes through the point P(10, 16) and it has vertices at (± 6, 0), then the equation of the normal to it at P is :

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 :