Let B the centre of the circle `x^(2) + y^(2) - 2x + 4y + 1 = 0`. Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then `8.(("area " Delta APQ)/("area " Delta BPQ))` is equal to ________.

Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0 .The tangents at the points B(1,7) and C(4,-2) on the circle meet at the point D .If Delta denotes the area of the quadrilateral ABCD,then (Delta)/(25) is equal to

Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0 . If the tangents at the points B (1, 7) and D(4, -2) on the circle meet at the point C, then the perimeter of the quadrilateral ABCD is

A line y=2x+c intersects the circle x^(2)+y^(2)-2x-4y+1=0 at P and Q. If the tangents at P and Q to the circle intersect at a right angle,then |c| is equal to

Tangents drawn from the point P(1,8) to the circle x^(2) + y^(2) - 6x - 4y -11=0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is:

Tangents are drawn to the hyperbola 4x^(2)-y^(2)=36 at the points P and Q . If these tangents intersect at the point T(0,3) and the area (in sq units) of Delta TPQ is a sqrt(5) then a=

Two tangents are drawn from the point P(-1,1) to the circle x^(2)+y^(2)-2x-6y+6=0 . If these tangen tstouch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to