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

Two concentric circles are given,where the equation of the smaller circle is $x^2 + y^2 = 4$. If each circle makes an intercept on the line $x + y = 2$ and the length of the intercept formed between the two circles is $1$,then the equation of the larger circle is:

Let a circle $C$ touch the lines $L_{1}: 4x - 3y + K_{1} = 0$ and $L_{2}: 4x - 3y + K_{2} = 0$,where $K_{1}, K_{2} \in R$. If a line passing through the centre of the circle $C$ intersects $L_{1}$ at $(-1, 2)$ and $L_{2}$ at $(3, -6)$,then the equation of the circle $C$ is:

The line $4x - 3y + 15 = 0$ intersects the circle $x^2 + y^2 - 6x - 8y = 0$ at two points $A$ and $B$. The maximum area of $\Delta ABC$,where $C$ is a point on the circumference of the circle,will be - .............. $sq. \ units$.

If $Q$ is the inverse point of $P(-1, 1)$ with respect to the circle $x^2+y^2-2x+2y=0$,then the line containing $Q$ is

$A$ line meets the circle $x^2+y^2-4x-4y-8=0$ at two points $A$ and $B$. If $P(2,-2)$ is a point on the circle such that $PA=PB=2$,then the equation of the line $AB$ is: