Mathematics Coordinate Geometry questions from JEE Main 2005.
An ellipse has $\mathrm{OB}$ as semi minor axis, $\mathrm{F}$ and $\mathrm{F}^{\prime}$ its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is
If a circle passes through the point $(a, b)$ and cuts the circle $x^2+y^2=p^2$ orthogonally, then the equation of the locus of its centre is
If a vertex of a triangle is $(1,1)$ and the mid-points of two sides through this vertex are $(-1,2)$ and $(3,2)$, then the centroid of the triangle is