Equation of a circle

For how many values of $p$, the circle $x^2 + y^2 + 2x + 4y - p = 0$ and the coordinate axes have exactly three common points?

Let $z\in\mathbb C$, the set of complex numbers. Then the equation, $2|z+3i|-|z-i|=0$ represents :

If a point P has co-ordinates (0, −2) and Q is any point on the circle, $x^2+y^2-5x-y+5=0$, then the maximum value of $(PQ)^2$ is :

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles $\cos^{-1}\left(\dfrac17\right)$ and $\sec^{-1}(7)$ at the centre respectively, then the distance between these chords, is :

The equation $\operatorname{Im}\left(\dfrac{iz-2}{z-i}\right)+1=0$, $z\in\mathbb C$, $z\ne i$ represents a part of a circle having radius equal to :

If one of the diameters of the circle, given by the equation, $x^2+y^2-4x+6y-12=0$, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is :

Let P be the point on the parabola, $y^2=8x$ which is at a minimum distance from the centre C of the circle, $x^2+(y+6)^2=1$. Then the equation of the circle, passing through C and having its centre at P is :

A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle ?

Let $P$ and $Q$ be distinct points on the parabola $y^2=2x$ such that a circle with $PQ$ as diameter passes through the vertex $O$ of the parabola. If $P$ lies in the first quadrant and the area of the triangle $\Delta OPQ$ is $3\sqrt2$, then which of the following is (are) the coordinates of $P$?

Locus of the image of the point (2, 3) in the line $(2x-3y+4)+k(x-2y+3)=0$, $k\in\mathbb R$, is a :

If $y+3x=0$ is the equation of a chord of the circle, $x^2+y^2-30x=0$, then the equation of the circle with this chord as diameter is :

If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is $3x+4y+3=0$, then the equation of the circumcircle of this triangle is :

If a circle passing through the point (−1, 0) touches $y$-axis at (0, 2), then the length of the chord of the circle along the $x$-axis is :

A circle $S$ passes through the point $(0,1)$ and is orthogonal to the circles $(x-1)^2+y^2=16$ and $x^2+y^2=1$. Then

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 :

If the differential equation representing the family of all circles touching $x$-axis at the origin is $\left(x^2-y^2\right)\dfrac{dy}{dx}=g(x)\,y$, then $g(x)$ equals :

If the point $(1,4)$ lies inside the circle $x^2+y^2-6x-10y+p=0$ and the circle does not touch or intersect the coordinate axes, then the set of all possible values of $p$ is the interval :

Let $L_1$ be the length of the common chord of the curves $x^2+y^2=9$ and $y^2=8x$, and $L_2$ be the length of the latus rectum of $y^2=8x$, then :

Circle(s) touching $x$-axis at a distance 3 from the origin and having an intercept of length $2\sqrt7$ on $y$-axis is (are)

Let $S$ be the focus of the parabola $y^2=8x$ and let $PQ$ be the common chord of the circle $x^2+y^2-2x-4y=0$ and the given parabola. The area of the triangle $PQS$ is