The common tangent to the circles x ² + y² = 4 and x² + y² + 6x + 8y – 24 = 0 also passes through the point :

If a tangent to the circle x² + y² = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

The tangent and the normal lines at the point ( $$\sqrt 3 $$, 1) to the circle x² + y² = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :

The sum of the squares of the lengths of the chords intercepted on the circle, x² + y² = 16, by the lines, x + y = n, n $$ \in $$ N, where N is the set of all natural numbers, is :