Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :

Tangents are drawn to the hyperbola 4x² - y² = 36 at the points P and Q.

If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $$\Delta $$PTQ is :

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :

Let $$\overrightarrow u $$ be a vector coplanar with the vectors $$\overrightarrow a = 2\widehat i + 3\widehat j - \widehat k$$ and $$\overrightarrow b = \widehat j + \widehat k$$. If $$\overrightarrow u $$ is perpendicular to $$\overrightarrow a $$ and $$\overrightarrow u .\overrightarrow b = 24$$, then $${\left| {\overrightarrow u } \right|^2}$$ is equal to