List of top Mathematics Questions on Circle

The area of the circle $x^2 + y^2 + 8x - 6y + c = 0$ is $75\pi$. Then the value of $c$ is equal to
The equation of a circle is \(x^2 + y^2 + 6x - 8y - 24 = 0\). If a chord of the circle subtends an angle of \(60^\circ\) at the centre of the circle, then the length of the chord is
If \((h,k)\) is the centre of a circle cutting three circles orthogonally, then \(\frac{3}{h}+\frac{1}{k}=\)
If \((h,k)\) is external centre of similitude of circles \[ x^2+y^2-6x-10y+9=0 \] and \[ x^2+y^2+6x+6y+2=0, \] then \(k-h=\)
Tangent to circle \(x^2+y^2-4x-8y-5=0\) equally inclined to axes is \(x+by+c=0\), \(b0\). Find \(2b+c\).
For circle \(x^2+y^2+12x-4y-9=0\), line \(x+2y-3=0\) represents
A circle makes intercepts \(2\sqrt7\) and \(2\sqrt{12}\) on axes and diameter lies on \(3x+2y=0\). Find a point on circle.
If \(\theta\) is the angle between the circles \[ x^{2}+y^{2}+2x-4y-4=0,\quad x^{2}+y^{2}-4x-6y-3=0 \] then \(\cos\theta=\)
If the circle $x^{2}+y^{2}-6x-12y-55=0$ intercepts the x-axis at two points $A$ and $B$, then $|AB|$ is equal to
The end-points of a diameter of a circle are (−1,4) and (5,4). Then the equation of the circle is
The number of common tangents to the circles \[ x^2+y^2-4x-6y-12=0,\quad x^2+y^2+6x+18y+26=0 \] is:
Let \( x-y=0 \) and \( x+y=1 \) be two perpendicular diameters of a circle of radius \( R \). The circle will pass through the origin if \( R \) equals:
The maximum number of common normals of \( y^2 = 4ax \) and \( x^2 = 4by \) is:
The locus of point of intersection of the tangents to the circle \( x^2 + y^2 = 16 \), such that the angle between them is 60°, is
If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$, then the coordinates of the point of contact are \dots
The least distance of the point A(10, 7) from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is length of seg AM. If MM' is the diameter of the circle, then the lengths of AM and AM' are respectively ______, ______ units.
The area of smaller part between the circle $x^2 + y^2 = 4$ and the line $x = 1$ is ______ sq. units.
The circumcenter of the triangle formed by lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is ______.
Two tangents to $x^{2}+y^{2}=4$ at A and B meet at $P(-4,0).$ Area of quadrilateral PAOB is}
If the tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + \text{C} = 0$, then C =}
If $f(x) = \frac{(27-2x)^{\frac{1}{3}} - 3}{9 - 3(243+5x)^{\frac{1}{5}}}, x \ne 0$ is continuous at $x = 0$, then the value of $f(0)$ is
The line \(y = mx + 3\) is tangent to the parabola \(y^2 = 4x\), if the value of m is
\(\cot^{-1} (2 \cos(2 \text{cosec}^{-1}(\sqrt{2}))) = \dots\)
If the tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + \text{C} = 0$, then C =}
If $f(x) = \frac{(27-2x)^{\frac{1}{3}} - 3}{9 - 3(243+5x)^{\frac{1}{5}}}, x \ne 0$ is continuous at $x = 0$, then the value of $f(0)$ is