The circle $x^2+y^2+4x-4y+4=0$ touches

Important Questions on Conic Sections

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

The equation of the circle concentric with the circle $x^2+y^2-6x-4y-12=0$ and touching $Y$-axis

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

Let $C$  be the circle with center at $\left(1,1\right)$ and radius $=1$. If $T$ is the circle centered at $\left(0,y\right)$, passing through the origin and touching the circle $C$ externally, then the radius of $T$ is equal to 

HARD

Mathematics>Coordinate Geometry>Conic Sections>Circle

A circle touching the $x-$ axis at $(3, 0)$ and making an intercept of length $8$ on the $y-$ axis passes through the point:

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16x+12y+c=0,$ then the value of $c$ is

HARD

Mathematics>Coordinate Geometry>Conic Sections>Circle

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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

A circle has radius $3$ and its centre lies on the line $y=x-1$. The equation of the circle, if it passes through $\left(7,3\right)$, is

HARD

Mathematics>Coordinate Geometry>Conic Sections>Circle

If a circle passing through the point $\left(-1, 0\right)$ touches $y$-axis at $\left(0, 2\right)$, then the $x$-intercept of the circle is 

HARD

Mathematics>Coordinate Geometry>Conic Sections>Circle

In a circle of radius $17 \mathrm{c}\mathrm{m},$ two parallel chords are drawn on opposite side of a diameter. The distance between the chords is $23 \mathrm{c}\mathrm{m}.$ If the length of one chord is $16 \mathrm{c}\mathrm{m},$ then the length of the other chord is

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

A circle with centre at $(3,6)$ passes through $(-1,1)$. Its equation is

HARD

Mathematics>Coordinate Geometry>Conic Sections>Circle

If the area of an equilateral triangle inscribed in the circle $x^2+y^2+10x+12y+c=0$ is $27\sqrt{3}\mathrm{sq}.\mathrm{units},$ then $c$ is equal to:

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

The centre and radius of the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}+2\mathrm{y}=0$ are

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

The intercept on the line $y=x$ by the circle $x^2+y^2-2x=0$ is $AB$ . The equation of the circle with $AB$ as a diameter is ……

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

The equation of the circle whose radius is $\sqrt{7}$ and concentric with the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-8\mathrm{x}+6\mathrm{y}-11=0$ is

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

If the coordinates of one end of a diameter of the circle $x^2+y^2-8x-4y+c=0$ are $\left(-3,2\right)$, then the coordinates at the other end are

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

If the lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to a circle, then radius of the circle is

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

The equation of the circle with centre $\left(2,2\right)$ which passes through $\left(4,5\right)$ is

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Circle

The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point

EASY

Mathematics>Coordinate Geometry>Conic Sections>Circle

Let $C_1$ and $C_2$ be the centres of the circles $x^2+y^2-2x-2y-2=0$ and $x^2+y^2-6x-6y+14=0$ respectively. If $P$ and $Q$ are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral $P{C}_{1}Q{C}_2$ is :