Circle and Syst...

A tangent PT is drawn to the circle x² + y² = 4 at the point P(√3, 1). A straight line L, perpendicular to PT is a tangent to the circle (x - 3)² + y² = 1
A common tangent of the two circle is

A tangent PT is drawn to the circle χ² + y² = 4 at the point P(√3, 1). A straight line L, perpendicular to PT is a tangent to the circle (χ - 3)² + y² = 1
A possible equation L is

The equation of the tangent from the point (0, 1) to the circle x² + y² - 2x - 6y + 6 = 0, is

If m₁ and m₂ are the slopes of tangents to the circle x² + y² = 4 from the point (3, 2), then m₁ - m₂ is equal to

The angle between the tangents dawn at the points (5, 12) and (12, - 5) to the circles x² + y² = 169 is

Tangents are drawn from the point (17, 7) to the circle x² + y² = 169²
Statement I The tangents are mutually perpendicular
Statement II The locus of the points from which mutually perpendicular tangents can be drawn to the given circles is x² + y² = 338

If 3x + y + k = 0 is a tangent to the circle x² + y² = 10, then the values of k are

From the point P(16, 7), tangents PQ and PR are drawn to circle x² + y² - 2x - 4y - 20 = 0. If C is the centre of the circle, then area of equilateral PQCR is

The condition for a line y = 2x + c to touch the circle x + y² = 16 is

The equation of the common tangent of the two touching circles, y² + x² - 6x -12y + 37 = 0 and x² + y² - 6y + 7 = 0 is