List of top Mathematics Questions on circle asked in MHT CET

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:
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 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 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.
Two tangents to the circle $x^{2}+y^{2}=4$ at the points A and B meet at the point $P(-4,0)$. Then the area of the quadrilateral PAOB, O being the origin, is
The centre of the circle whose radius is 3 units and touching internally the circle $x^2 + y^2 - 4x - 6y - 12 = 0$ at the point $(-1, -1)$ is
The equation of a circle that passes through the origin and cut off intercepts $-2$ and $3$ on the X-axis and Y-axis respectively is
Two circles centred at $(2,3)$ and $(4,5)$ intersect each other. If their radii are equal, then the equation of the common chord is
If a circle passes through the points $(0,0)$, $(x, 0)$ and $(0, y)$, then the coordinates of its centre are
The equation of the common tangent to the circles $x^2 + y^2 - 4x + 10y + 20 = 0$ and $x^2 + y^2 + 8x - 6y - 24 = 0$ is
Equation of the chord of the circle $x^2 + y^2 - 4x - 10y + 25 = 0$ having mid-point $(1, 2)$ is
The equation of the circle whose centre lies on the line $x-4y=1$ and which passes through the points $(3,7)$ and $(5,5)$ is
The equation of circle with centre at \( (2, -3) \) and the circumference \( 10\pi \) units is
The equation of tangent to the circle $x^2+y^2=64$ at the point $P\left(\frac{2\pi}{3}\right)$ is
If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to a circle, then the radius of the circle is
The equation of the circle whose centre lies on the line $x-4y=1$ and which passes through the points $(3,7)$ and $(5,5)$ is
If the line \( x - 2y = m \, (m \in \mathbb{Z}) \) intersects the circle \( x^{2} + y^{2} = 2x + 4y \) at two distinct points, then the number of possible values of \( m \) are