Statement 1 : The number of circles touching lines `x+y=1,2x-y=5,` and `3x+5y-1=0` is four Statement 2 : In any triangle, four circles can be drawn touching all the three sides of the triangle.

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

Statement 1 : The center of the circle having x+y=3 and x-y=1 as its normals is (1, 2) Statement 2 : The normals to the circle always pass through its center

Statement 1 : The locus of the center of a variable circle touching two circle (x-1)^2+(y-2)^2=25 and (x-2)^2+(y-1)^2=16 is an ellipse. Statement 2 : If a circle S_2=0 lies completely inside the circle S_1=0 , then the locus of the center of a variable circle S=0 that touches both the circles is an ellipse.

Statement 1 : The equations of tangents to the hyperbola 2x^2-3y^2=6 which is parallel to the line y=3x+4 are y=3x-5 and y=3x+5. Statement 2 : For a given slope, two parallel tangents can be drawn to the hyperbola.

The centre of the smallest circle touching the circles x^2+ y^2-2y -3=0 and x^2 +y^ 2-8x -18y +93= 0 is:

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1

Consider: L_1:2x+3y+p-3=0 L_2:2x+3y+p+3=0 where p is a real number and C : x^2+y^2+6x-10 y+30=0 Statement 1 : If line L_1 is a chord of circle C , then line L_2 is not always a diameter of circle Cdot Statement 2 : If line L_1 is a a diameter of circle C , then line L_2 is not a chord of circle Cdot (A) Both the statement are True and Statement 2 is the correct explanation of Statement 1. (B) Both the statement are True but Statement 2 is not the correct explanation of Statement 1. (C) Statement 1 is True and Statement 2 is False. (D) Statement 1 is False and Statement 2 is True.

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

The radius of the of circle touching the line 2x + 3y +1 = 0 at (1,-1) and cutting orthogonally the circle having line segment joining (0, 3) and (-2,-1) as diameter is

2x+y=0 is the equation of a diameter of the circle which touches the lines 4x-3y+10=0 and 4x-3y-30=0. The centre and radius of the circle are