If the circles x² + y² + 5Kx + 2y + K = 0 and 2(x² + y²) + 2Kx + 3y –1 = 0, (K$$ \in $$R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for :

A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (–8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :

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 :