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 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.

Statement 1 : Any chord of the conic x^2+y^2+x y=1 through (0, 0) is bisected at (0, 0). Statement 2 : The center of a conic is a point through which every chord is bisected.

If (1,-3) is the centre of the circle x^(2) + y^(2) +ax + by + 9 =0 its radius is

Find the center of the circle x=-1+2costheta,y=3+2sintheta

Consider two circles x^2+y^2-4x-6y-8=0 and x^2+y^2-2x-3=0 Statement 1 : Both the circles intersect each other at two distinct points. Statement 2 : The sum of radii of the two circles is greater than the distance between their centers.

Statement 1: The line x-y-5=0 cannot be normal to the parabola (5x-15)^2+(5y+10)^2=(3x-4y+2)^2dot Statement 2: Normal to parabola never passes through its focus.

Statement 1 : Let S_1: x^2+y^2-10 x-12 y-39=0, S_2 x^2+y^2-2x-4y+1=0 and S_3:2x^2+2y^2-20 x-24 y-78=0. The radical center of these circles taken pairwise is (-2,-3)dot Statement 2 : The point of intersection of three radical axes of three circles taken in pairs is known as the radical center.

The center(s) of the circle(s) passing through the points (0, 0) and (1, 0) and touching the circle x^2+y^2=9 is (are)

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.

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these