Circle and Syst...

If the two circles x² + 2y² - 2x + 22y + 5 = 0 and x² + y² + 14x + 6y + k = 0 intersect orthogonally, then k is equal to

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² - 3ax + dy - 1 = 0 intersect in two distinct points P and Q, then the line 5x + by - a = 0 passes through P and Q for

If a circle passes through the point (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is

The shortest distance of the point (6, –8) from the circle x² + y² = 36, is

The number of feet of normals from the point (7, –4) to the circle x² + y² = 5 is

The number of common tangents of the circles (x + 3)² + (y – 2) )² = 49 and (x – 2) )² + (y + 1) )² = 4

The radius of the circle passing thro’ the point P(6, 2), two of whose diameters are x + y =6 and x + 2y = 4 is

If the centroid of an equilateral triangle is (1, 1) and its one vertex is (-1, 2), then the equation of its circumcircle is

Two circles, each of radius 5, have a common tangent at (1,1) whose equation is 3x + 4y – 7 = 0 Then their centres are