If the angles of a triangle are in the ratio $$4:1:1$$, then the ratio of the longest side to the perimeter is

The focal chord to $${y^2} = 16x$$ is tangent to $${\left( {x - 6} \right)^2} + {y^2} = 2,$$ then the possible values of the slope of the chord, are

For hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$ which of the following remains constant with change in $$'\alpha '$$

The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1,$$ is