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

a circle passing through the point (2,2(sqrt2-1)) touches the pair of lines x^2 -y^2 -4x+4 =0 . The centre of the circle is

If the line 2x-y+1=0 touches the circle at the point (2,5) and the centre of the circle lies in the line x+y-9=0. Find the equation of the circle.

A foot of the normal from the point (4, 3) to a circle is (2, 1) and a diameter of the circle has the equation 2x -y -2 =0 . Then the equation of the circle is:

The normal at the point (3, 4) on a circle cuts the circle at the point (-1,-2). Then the equation of the circle is

Show that the equation of a line passing through the point (11,-2) and touching the circle x^(2)+y^(2)=25 is 3x+4y=25 .

P(sqrt2,sqrt2) is a point on the circle x^2+y^2=4 and Q is another point on the circle such that arc PQ= 1/4 circumference. The co-ordinates of Q are

A ray of light incident at the point (-2, -1) gets reflected from the tangent at (0, -1) to the circle x^2 +y^2=1 . The reflected ray touches the circle. The equation of the line along which the incident ray moved is

A circle of radius unity is centered at thet origin. Two particles tart moving at the same time from the point (1, 0) and move around the circle in opposite direction. One of the particle moves anticlockwise with constant speed v and the other moves clockwise with constant speed 3v . After leaving (1, 0) , the two particles meet first at a point P, and continue until they meet next at point Q . The coordinates of the point Q are

The equation of a circle is x^2+y^2=4. Find the center of the smallest circle touching the circle and the line x+y=5sqrt(2)

The equation of a circle is x^2+y^2=4. Find the center of the smallest circle touching the circle and the line x+y=5sqrt(2)