`A(1/(sqrt(2)),1/(sqrt(2)))` is a point on the circle `x^2+y^2=1` and `B` is another point on the circle such that are length `A B=pi/2` units. Then, the coordinates of `B` can be

(1, 2sqrt2) is a point on circle, x^2 + y^2 = 9 . Which of the following is not the point on the circle at 2 units distance from (1, 2sqrt2) ?

Find the points on the unit circle x^(2)+y^(2)=1 nearest and farthest from (1,1)

A particle from the point P(sqrt3,1) moves on the circle x^2 +y^2=4 and after covering a quarter of the circle leaves it tangentially. The equation of a line along with the point moves after leaving the circle is

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

Let p,q be chosen one by one from the set {1, sqrt(2),sqrt(3), 2, e, pi} with replacement. Now a circle is drawn taking (p,q) as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)

If m(x-2)+sqrt(1-m^2) y= 3 , is tangent to a circle for all m in [-1, 1] then the radius of the circle is

Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it at the point A in the first quadrant. Find the coordinates of another point B on the circle such that A B=4 .

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is