The coordinates of the focus of the parabola described parametrically by $$x=5t^2+2$$ and $$y=10t+4$$ (where t is a parameter) are

If $$\tan \theta_1, \tan \theta_2=\frac{-a^2}{b^2}$$, then the chord joining 2 points $$\theta_1$$ and $$\theta_2$$ one the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ will subtend a right angle at

If one focus of a hyperbola is $$(3,0)$$, the equation of its directrix is $$4 x-3 y-3=0$$ and its eccentricity $$e=5 / 4$$, then the coordinates of its vertex is

If the vertices of the triangles are (1, 2, 3), (2, 3, 1), (3, 1, 2) and if H, G, S and I respectively denote its orthocentre, centroid, circumcentre and incentre, then H + G + S + I is equal to