Let `C_1 : x^2 + y^2-2x = 0` and `C_2 : x^2 + y^2-2x-1=0.` If `P` is a point on `C_2` and PA and PB are the tangents to the circle `C_1` then angle between these two tangents is

If two tangents are drawn from a point on x^(2)+y^(2)=16 to the circle x^(2)+y^(2)=8 then the angle between the tangents is

The equations of two circles are x^(2)+y^(2)+2 lambda x+5=0 and x^(2)+y^(2)+2 lambda y+5=0 .P is any point on the line x-y=0 .If PA and PB are the lengths of the tangents from P to the two circles and PA=3 them PB=

The equations of two circles are x^(2)+y^(2)+2 lambda x+5=0 and x^(2)+y^(2)+2 lambda y+5=0.P is any point on the line x-y=0. If PA and PB are the lengths of the tangent from Ptothe circles and PA=3 then find PB.

Let C_(1):x^(2)+y^(2)-2x+2y=0 and C-2:x^(2)+y^(2)-2x+2y=0 are two given circles.From a moving poont P on C_(2), tangents are drawn to C_(1) at A and B.The locus of orthocentre of Delta PAB is

Consider circles C_1 : x^2 +y^2 + 2x-2y + p = 0, C_2 : x^2+y^2-2x+2y-p=0 and C_3 : x^2+y^2=p^2 Statement I: If the circle C_3 intersects C_1, orthogonally then C_2 does not represent a circle Statement II: If the circle C_3, intersects C_2 orthogonally then C_2 and C_3 have equal radii. Then which of the following statements is true ?

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

From the point P(4,-4) tangents PA and PB are drawn to the circle x^(2)+y^(2)-6x+2y+5=0 whose centre is C then Length of AB

Let C_(1) and C_(2) be the circles x^(2) + y^(2) - 2x - 2y - 2 = 0 and x^(2) + y^(2) - 6x - 6y + 14 = 0 respectively. If P and Q are points of intersection of these circles, then the area (in sq. units ) of the quadrilateral PC_(1) QC_(2) is :

If y=c is a tangent to the circle x^(2)+y^(2)-2x-2y-2=0, then the value of c can be