Circle

Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2 y=\frac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $\mathrm{C}$, makes an angle of $\frac{\pi}{4}$ with the line $\mathrm{CP}$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $P Q R$ (in unit $^{2}$ ) is :

The centres of a set of circles, each of radius 3, lie on the circle ${x^2}\, + \,{y^2} = 25$. The locus of any point in the set is :

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is :

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is :

Choose the correct statement about two circles whose equations are given below : x² + y² $-$ 10x $-$ 10y + 41 = 0 x² + y² $-$ 22x $-$ 10y + 137 = 0

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

The differential equation of the family of circles with fixed radius $5$ units and centre on the line $y = 2$ is :

If $P$ and $Q$ are the points of intersection of the circles ${x^2} + {y^2} + 3x + 7y + 2p - 5 = 0$ and ${x^2} + {y^2} + 2x + 2y - {p^2} = 0$ then there is a circle passing through $P,Q$ and $(1, 1)$ for :

The centres of those circles which touch the circle, ${x^2} + {y^2} - 8x - 8y - 4 = 0$, externally and also touch the $x$-axis, lie on :

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, $y - 4x + 3 = 0,$ then its radius is equal to :