If two circles `(x-1)^2+(y-3)^2=r^2` and `x^2+y^2-8x+2y+8=0` intersect in two distinct points then

The circles x^(2)+y^(2)-10x+16=0 and x^(2)+y^(2)=a^(2) intersect at two distinct points if

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 m .

The circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect at an angle of

If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersects at points P and Q , then find the values of a for which the line 5x+b y-a=0 passes through Pa n dQdot

The circle x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect at an angle of :

The circle with equation x^2 +y^2 = 1 intersects the line y= 7x+5 at two distinct points A and B. Let C be the point at which the positive x-axis intersects the circle. The angle ACB is

Two circle x^2+y^2=6 and x^2+y^2-6x+8=0 are given. Then the equation of the circle through their points of intersection and the point (1, 1) is x^2+y^2-6x+4=0 x^2+y^2-3x+1=0 x^2+y^2-4y+2=0 none of these

The circle x^2+y^2-8x = 0 and hyperbola x^2 /9 - y^2 /4=1 intersect at the points A and B. Then the equation of the circle with AB as its diameter is

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. (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

If the two circles 2x^(2) +2y^(2) -3x+6y+k=0 and x^(2) +y^(2) -4x +10y +16=0 cut orthogonally, then the vlaue of k is-