Let the focal chord of the parabola $$\mathrm{P}: y^{2}=4 x$$ along the line $$\mathrm{L}: y=\mathrm{m} x+\mathrm{c}, \mathrm{m}>0$$ meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola $$\mathrm{H}: x^{2}-y^{2}=4$$. If O is the vertex of P and F is the focus of H on the positive x-axis, then the area of the quadrilateral OMFN is :

If the tangents drawn at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the parabola $$y^{2}=2 x-3$$ intersect at the point $$R(0,1)$$, then the orthocentre of the triangle $$P Q R$$ is :

If the length of the latus rectum of a parabola, whose focus is $$(a, a)$$ and the tangent at its vertex is $$x+y=a$$, is 16, then $$|a|$$ is equal to :

Let $$P(a, b)$$ be a point on the parabola $$y^{2}=8 x$$ such that the tangent at $$P$$ passes through the centre of the circle $$x^{2}+y^{2}-10 x-14 y+65=0$$. Let $$A$$ be the product of all possible values of $$a$$ and $$B$$ be the product of all possible values of $$b$$. Then the value of $$A+B$$ is equal to :