The given circle $x^2 + y^2 + 2px = 0$,$p \in R$ touches the parabola $y^2 = 4x$ externally,then

If the line $ax + y = c$ touches both the curves $x^2 + y^2 = 1$ and $y^2 = 4\sqrt{2}x$,then $|c|$ is equal to

For a circle of diameter $R$,touching the circle $x^2 + y^2 - 4y = 0$ and passing through the point $(4, 5)$,which of the following is correct?

The equations of the circles which touch the lines $3x - 4y + 1 = 0$ and $4x + 3y - 7 = 0$ and pass through the point $(2, 3)$ are:

Three circles lie on a plane such that each of them externally touches the other two. Two of them have radius $3$,and the third has radius $1$. If $A, B$,and $C$ are the points of tangency of the circles,then the area of the triangle $ABC$ is

Two circles each of radius $5$ units touch each other at $(1,2)$ and $4x+3y=10$ is their common tangent. The equation of that circle among the two given circles,such that some portion of it lies in every quadrant is