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

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.

The circle x^2 + y^2 - 3x - 4y + 2 = 0 cuts the x axis at the points

The point of contact of the tangent 2x+3y+9=0 to the parabola y^(2)=8x is:

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

Show that the line x-y + 4 =0 is a tangents to the ellipse x^(2) + 3y^(2) =12 . Also find the coordinates of the points of contact.

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

If the circles x^2+y^2-9=0 and x^2+y^2+2alpha x+2y+1=0 touch each other, then alpha is (a) -4/3 (b) 0 (c) 1 (d) 4/3

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

At what points on the curve x^(2)+y^(2) - 2x -4y+1=0 the tangent is parallel to Y-axis.