List of top Mathematics Questions on circle

The parametric equations of the circle $x^2 + y^2 - 4x - 6y - 12 = 0$ are:
The parametric equations of the circle $x^2 + y^2 - 4x - 6y - 12 = 0$ are:
The equation of a circle whose Centre is \((2,-1)\) and which passes through the point \((3,6)\) is
The equation of a circle whose Centre is \((-3,2)\) and area is \(176\) units is
If the one end of a diameter of the circle $x^2 + y^2 + 3x + y - 6 = 0$ is at $(-4,-2)$, then the other end of the diameter is at
The three vertices of a triangle are \( (0,0) \), \( (3,1) \) and \( (1,3) \). If this triangle is inscribed in a circle, then the equation of the circle is
The circle passing through the point (1, -2) and touching the x-axis at (3,0) also passes through the point
The value of \(k\), if the circles \(2x^{2} + 2y^{2} - 4x + 6y = 3\) and \(x^{2} + y^{2} + kx + y = 0\) cut orthogonally is
The locus of the mid-point of a chord of the circle \( x^2 + y^2 = 4 \), which subtends a right angle at the origin is
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 length of radius of 'S' is ________ units.
The equation of the circle passing through the point $(1, 1)$ and having two diameters along the pair of lines $x^2 - y^2 - 2x + 4y - 3 = 0$ is
If the two circles \( (x-2)^2+(y-3)^2=9 \) and \( (x-2)^2+(y+3)^2=a^2 \) intersect in two distinct points, then
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 length of radius of 'S' is ________ units.
If two diameters of a circle are along the lines $2x-3y=5$ and $3x-4y=7$, then the centre is at
A circle touches the \( x \)-axis at \( (9,0) \). If it also touches the straight line \( y = 14 \), then the equation of the circle is
If length of the tangent is \(8\text{ cm}\) and the distance between the center of the circle and the external point is \(11\text{ cm}\), then the area of the circle is
In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
The length of the tangent from the point \((5,1)\) to the circle \(x^2+y^2+6x-4y-3=0\) is
If length of the tangent is \(8\text{ cm}\) and the distance between the center of the circle and the external point is \(11\text{ cm}\), then the area of the circle is
The length of the tangent from the point \((5,1)\) to the circle \(x^2+y^2+6x-4y-3=0\) is
In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
The least area of a circle circumscribing any right-angle triangle of area \( \frac{9}{\pi} \) square units is:
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 length of radius of 'S' is ________ units.
The line $x + y = 2$ touches a circle. If the centre of the circle is at $(-4,\,0)$, then the radius of the circle is
The equation of the line passing through the point $(-4,\,2)$ and the centre of the circle $2x^2 + 2y^2 - 8y = 7$ is