Statement 1 : Circles `x^2+y^2=144` and `x^2+y^2-6x-8y=0` do not have any common tangent. Statement 2 : If two circles are concentric, then they do not hav common tangents.

The circles x^2+y^2 +2x +4y-20=0 and x^2 +y^2 + 6x-8y + 10 = 0 a) are such that the number of common tangents on them is 2 b) are orthogonal c) are such that the length of their common tangents is 5(12/5)^(1/4) d) are such that the length of their common chord is 5sqrt3/2

Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

Find the coordinates of the point at which the circles x^2-y^2-4x-2y+4=0 and x^2+y^2-12 x-8y+36=0 touch each other. Also, find equations of common tangents touching the circles the distinct points.

Statement 1 : If two circles x^2+y^2+2gx+2fy=0 and x^2+y^2+2g^(prime)x+2f^(prime)y=0 touch each other, then f^(prime)g=fg^(prime)dot Statement 2 : Two circles touch other if the line joining their centers is perpendicular to all possible common tangents.

There are two circles whose equation are x^2+y^2=9 and x^2+y^2-8x-6y+n^2=0,n in Zdot If the two circles have exactly two common tangents, then the number of possible values of n is 2 (b) 8 (c) 9 (d) none of these

Tangents are drawn from the origin to the circle x^2+y^2-2h x-2h y+h^2=0,(hgeq0) Statement 1 : Angle between the tangents is pi/2 Statement 2 : The given circle is touching the coordinate axes.

A tangent is drawn to each of the circles x^2+y^2=a^2 and x^2+y^2=b^2dot Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

The number of common tangents to the circles x^(2) + y^(2) = 4 and x^(2)+y^(2)-6x-8y=24 is

From a pt A common tangents are drawn to a circle x^2 +y^2 = a^2/2 and y^2 = 4ax . Find the area of the quadrilateral formed by common tangents, chord of contact of circle and chord of contact of parabola.

The circles x^2+y^2-2x-4y+1=0 and x^2+y^2+4x+4y-1=0 (a)touch internally (b)touch externally (c)have 3x+4y-1=0 as the common tangent at the point of contact (d)have 3x+4y+1=0 as the common tangent at the point of contact