Circles practice · Easy

Equation of a circle with centre $(-4,3)$ touching internally and containing the circle $x^2+y^2=1$ is

The number of common tangents to the circles $x^2+y^2=4$ and $x^2+y^2-6 x-8 y=24$, is

A circle is passing through the points $A(1,1)$ and $B(1,3)$ and the bisector of first and third quadrant is normal to it, then its area, in square units, is

If tangents $P A$ and $P B$ are drawn to $x^2+y^2=9$ from the point $P(4,4)$, then area of $\triangle O A B, O$ being the origin, is equal to

The circles $x^2+y^2-10 x+16=0$ and $x^2+y^2=r^2$ intersect each other in two distinct points if

Find the intercept made by the circle $x^2+y^2-14 x-10 y+23=0$ on the line $7 x+y-4=0$.

The locus of pole of any tangent to the circle $x^2+y^2$ $=4$ w.r.t. the hyperbola $x^2-y^2=4$ is the circle

If the circles ${x^2} + {y^2} + 2gx + 2fy = 0$ and ${x^2} + {y^2} + 2g'\,x + 2f'\,y = 0$ touch each other, then

The circle described on the line joining the points $(0,1),(a, b)$ as diameter cuts the $x$-axis in points whose abscissae are roots of the equation

The tangents to the circle $x^2+y^2=48$, which are inclined at angle of $60^{\circ}$ with the axis of $x$ form a rhombus, the length of whose sides is

The number of common tangents to the circles ${x^2} + {y^2} - y = 0$ and ${x^2} + {y^2} + y = 0$ is

If the chords of contact of the tangents from a point on the circle ${x^2} + {y^2} = {a^2}$ to the circle ${x^2} + {y^2} = {b^2}$ touch the circle ${x^2} + {y^2} = {c^2},$ then the roots of the equation $a{x^2} + 2bx + c = 0$, are

A line through $P\left( {1,4} \right)$ intersect a circle ${x^2} + {y^2} = 16$ at $A$ and $B$, then $PA.PB$ is equal to

If the base of a triangle and the ratio of the lengths of the other two unequal sides are given, then the vertex lies on a/an

The value of $c$, for which the line $y = 2x + c$ is a tangent to the circle ${x^2} + {y^2} = 16$, is

Two circles ${x^2} + {y^2} - 2x - 3 = 0$ and ${x^2} + {y^2} - 4x - 6y - 8 = 0$ are such that

If the area of the circle $4{x^2} + 4{y^2} - 8x + 16y + k = 0$ is $9\pi$ sq unit, then the value of $k$ is

If the abscissa and the ordinates of two points $A$ and $B$ are the roots of the equations $x^2+2 a x-b^2=0$ and $y^2+2 p y-q^2=0$ respectively.
Then, the equation of circle with $A B$ as diameter is

Find the radius of the circle whose centre is in fourth quadrant and which touches as each of the three lines $x=0$, $y=0$ and $3 x+4 y-12=0.$

Find the parametric equations of the circle $x^2+y^2-4 x-2 y+$ $1=0$.

The equation of the tangent to the circle ${x^2} + {y^2} = 4$, which are parallel to $x + 2y + 3 = 0$, are

If the equation of the circle is $x^2+y^2-8 x+10 y-12=0$, then

I. Centre of the circle is $(4,-5)$.

II. Radius of the circle is $\sqrt{53}$.

Let a circle $C_{1}$ be obtained on rolling the circle $x^{2}+$ $y^{2}-4 x-6 y+11=0$ upwards 4 units on the tangent $T$ to it at the point $(3,2)$. Let $C_{2}$ be the image of $C_{1}$ in $T$. Let $A$ and $B$ be the centers of circles $C_{1}$ and $C_{2}$ respectively, and $M$ and $N$ be respectively the feet of perpendiculars drawn from $A$ and $B$ on the $x$-axis. Then the area of the trapezium AMNB is:

The locus of a point which moves so that the ratio of the length of the tangents to the circles ${x^2} + {y^2} + 4x + 3 = 0$ and ${x^2} + {y^2} - 6x + 5 = 0$ is $2:3$, is

Discuss the position of the points $(1,2)$ and $(6,0)$ with respect to the circle $x^2+y^2-4 x+2 y-11=0$.

Equation of a circle with centre $C(h, k)$ and radius 5 such that $h^2-3 h+2=0$ and $k^2+5 k-6=0$ is

The area of the circle whose centre is at $\left( {2,3} \right)$ and passing through $\left( {4,6} \right)$, is

The locus of the centres of the circles for which one end of a diameter is $(1,1)$ while the other end is on the line $x+y=3$, is

The line $3x - 2y = k$ meets the circle ${x^2} + {y^2} = 4{r^2}$ at only one point if ${k^2}$ is equal to

The equation of the circle which touches the axes of the coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is ${x^2} + {y^2} - 2cx - 2cy + {c^2} = 0,$ where $c$ is