If circles `x^(2)+y^(2)=c` with radius `sqrt(3) and x^(2)+y^(2)+ax+by+c=0` with radius `sqrt(6)` intersect at two points A and B. If length of `AB=sqrt(l)`. Find `l`.

Given two circles x^(2)+y^(2)+3sqrt(2)(x+y)=0 and x^(2)+y^(2)+5sqrt(2)(x+y)=0. Let the radius of the third circle,which touches the two given circles and to their common diameter,be (2 lambda-1)/(lambda) The value of lambda is

If x^2/a^2+y^2/b^2=1 passes through (sqrt(3/2),1) , e=1/sqrt3 , circle centred at one of the focus and radius 2/sqrt3 . these ellipse and circle intersect at two points . Find square of the distance between the two points is

A straight line through the point (2, 2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the points A and B. The equation of the line AB so that DeltaOAB is equilateral, is:

A straight line through the point (2, 2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is

A st. line through the point (2, 2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is :

A straight line through the point (2, 2) intersects the lines sqrt3x + y = 0 and sqrt3 x-y=0 at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is ,

Any circle through the point of intersection of the lines x+sqrt(3)y=1 and sqrt(3)x-y=2 intersects these lines at points Pa n dQ . Then the angle subtended by the arc P Q at its center is 180^0 (b) 90^0 (c) 120^0 depends on center and radius