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.

If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two distinct points, then find the values of mdot

Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect.

If the two circles 2x^2+2y^2-3x+6y+k=0 and x^2+y^2-4x+10 y+16=0 cut orthogonally, then find the value of k .

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

The circles x^2+y^2-12 x-12 y=0 and x^2+y^2+6x+6y=0. touch each other externally touch each other internally intersect at two points none of these

Consider the circles x^2+(y-1)^2=9,(x-1)^2+y^2=25. They are such that these circles touch each other one of these circles lies entirely inside the other each of these circles lies outside the other they intersect at two points.

The circle x^(2) + y^(2) = 4 x + 8 y + 5 intersects the line 3x -4y =m at two distinct points if

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 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