Circle and Syst...

If x/α + y/β = 1 touches the circles x² + y² = a², then point (1/α, 1/β) lies on a/ am

Angle between tangents drawn to circles x² + y² = 20, from the point (6, 2) is

The locus of a point which moves, so that the ratio of the length of the tangents to the circle x² + y² + 4x + 3 = 0 and x² + y² - 6x + 5 = 0 is 2 : 3 is

Two tangents to the circle x² + y² = 4 at the points A and B meet at P(-4, 0). The area of the quadrilateral PAOB, where O is the origin, is

If y = 3x is the tangent to a circle with centre (1, 1), then the other tangent drawn through (0, 0) to the circle is

The equations of the tangents to circle 5x² + 5y² = 1, parallel to line 3x + 4y = 1 are

The measure of the chord intercepted circle x² + y² = 9 and the line x - y + 2 = 0 is

The location for the l₁x + m₁y + n₁ = 0 to be conjugate with respect to the circle x² + y² = r², is

The locus of the mid - points of the chord of the circle x² + y² = 4 which subtends a right angle at the origin is

The locus of the point of intersection of the tangents at the extremeties of a chord of the circle x² + y² - 2ax = 0 passes throught the point, is