List of top Mathematics Questions on circle

If the circle $x^2 + y^2 - 4x - 6y + \lambda = 0$ touches the x-axis, then the value of $\lambda$ is:

If the circle $x^2 + y^2 + 2x - 2y + c = 0$ cuts the circle $x^2 + y^2 - 4x - 6y + 11 = 0$ orthogonally, then the value of $c$ is:

If the lines joining the origin to the points of intersection of the line $y = mx + 1$ and the circle $x^2 + y^2 = 1$ are perpendicular to each other, then the value of $m^2$ is:

If the equation \[ x^2-6x+y^2+8y+9=0 \] represents a circle, then its radius is:

The equation of a circle whose center lies on \(x+2y = 0\) and touching the lines \(3x-4y+8 = 0\) and \(3x-4y-28 = 0\) is

The equation of the circle which passes through the points \((2,3)\) and \((4,5)\) and whose centre lies on a straight line \(4x-y-3 = 0\), is

A circle passes through the point \((0,1)\) and touches the parabola \(y = x^2\) at the point \((1,1)\). The centre of the circle is...

Let PA and PB be the tangent segments drawn from point P\((6,8)\) to the circle with the centre at origin O. The radius of circle for which the area of quadrilateral PAOB is maximum, is...

A line making equal intercepts on coordinate axes and is tangent to the circle \(x^2+y^2 = 4\). The length of each intercept made by line on the coordinate axes is ...

The number of circles passing through the origin and touching the lines \(x+y = 1\) and \(x-y = 1\) is \(\ldots\)

The area of the region (in sq. unit) bounded by x-axis, the tangent and normal to the circle \(x^2+y^2 = 4\), drawn at a point \((1,\sqrt{3})\) is

The tangent to the circle \(x^2+y^2 = 10\) at the point \((3,1)\) touches the circle \(x^2+y^2-2\sqrt{10}\,x-20y+k = 0\), then the value of \(k\) is...

The statement pattern \([(p∧q)\rightarrow (\sim p∨r)]∨[(\sim p∨r)\rightarrow (p∧q)]\) is

If a circle passes through the points \((2,3)\) and \((4,5)\) and its center lies on the straight line \(y-4x+3 = 0\), then its equation is......

Line \(l:x+y = 4\) intersects the circle \(x^2+y^2-2x-2y = 2\) at points \(A\) and \(B\). If C is the center of the circle, then the area of \(△ABC\) is...

The equations of the tangent to the curve \(x^2+y^2 = 10\), where the tangent is parallel to the line \(2x+y-1 = 0\), are

The angle between the tangents drawn from the origin to the circle \((x-7)^2+(y+1)^2 = 25\) is

The equation of a circle which passes through the points \((2,3)\) and \((4,5)\) and whose center lies on the straight line \(y-4x+3 = 0\) is

If \(P(3,4)\) is a fixed point and \(Q\) is a variable point on the circle \[ x^2+y^2=16, \] then the locus of the midpoint of \(PQ\) is

The equations of two circles which touch the coordinate axes and whose centres lie on the line \[ x-2y=3 \] 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

The length of the intercept made by the circle $x^2 + y^2 - 10x + 4y + 9 = 0$ on the x-axis is:

The length of the tangent from the point $(3, 4)$ to the circle $x^2 + y^2 - 2x - 4y + 1 = 0$ is:

The equation of the common chord of the circles $x^2 + y^2 - 4x - 4y = 0$ and $x^2 + y^2 - 6x - 8y + 10 = 0$ is: