Consider a family of circles which are passing through the point $\left(-1,1\right)$and are tangent to x-axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

The point diametrically opposite to the point P (1, 0) on the circle $x^2+y^2+2x+4y-3=0$is

If P and Q are the points of intersection of the circles $x^2+y^2+3x+7y+2p5=0$and $x^2+y^2+2x+2y{p}^2=0$, then there is a circle passingthrough P, Q and $\left(1,1\right)$for

hree distinct points A, B and C are given in the 2 - ditmensional c pla nt the poi ne such that the ratio of the distance of any one of them from (1, 0) to the distance from the point (-1, 0) is equal to circumcentre of the triangle ABC is at the point 3 JEE 2009]

The circle $x^2+y^2=4x+8y+5$intersects the line $3x4y=m$at two distinct points if

The two circles $x^2+y^2=ax$and $x^2+y^2=c^2\left(c>0\right)$touch each other if :

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having centre at (0, 3) is

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to