The equation of a circle is `S_(1)-=x^(2)+y^(2)=1` .The orthogonal tangents to `S_(1)`meet at another circle `S_(2)` and the orthogonal tangents to `S_(2)` meet at the third circle `S_(3)` .Then:

The equation of a circle S_1 is x^2 + y^2 = 1 . The orthogonal tangents to S_1 meet at another circle S_2 and the orthogonal tangents to S_2 meet at the third circle S_3 . Then (A) radius of S_2 and S_3 are in ratio 1 : sqrt(2) (B) radius of S_2 and S_1 are in ratio 1 : 2 (C) the circles S_1, S_2 and S_3 are concentric (D) none of these

The equation of a circle C_1 is x^2+y^2= 4 . The locus of the intersection of orthogonal tangents to the circle is the curve C_2 and the locus of the intersection of perpendicular tangents to the curve C_2 is the curve C_3 , Then

Find the equation of the circle which cuts the circle x^(2)+y^(2)+5x+7y-4=0 orthogonally, has its centre on the line x=2 and passes through the point (4,-1).

The equation of the tangent to the circle x^(2)+y^(2)-4x+4y-2=0 at (1,1) is

A tangent to the circle x^(2)+y^(2)=1 through the point (0, 5) cuts the circle x^(2)+y^(2)=4 at P and Q. If the tangents to the circle x^(2)+y^(2)=4 at P and Q meet at R, then the coordinates of R are

inside the circles x^2+y^2=1 there are three circles of equal radius a tangent to each other and to s the value of a equals to

Let RS be the diameter of the circle x^2+y^2=1, where S is the point (1,0) Let P be a variable apoint (other than R and S ) on the circle and tangents to the circle at S and P meet at the point Q.The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. then the locus of E passes through the point(s)- (A) (1/3,1/sqrt3) (B) (1/4,1/2) (C) (1/3,-1/sqrt3) (D) (1/4,-1/2)

Circle S_(1) is centered at (0,3) with radius 1. Circle S_(2) is externally tangent to circle S_(1) and also tangent to x-axis.If the locus of the centre of the variable circle S_(2) can be expressed as y =1+ ( x^(2))/( lambda) . Find lambda

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

If a circle passes through the point (1, 1) and cuts the circle x^(2)+y^(2)=1 orthogonally, then the locus of its centre is