Circle

The radius of a circle is $\mathbf{5 ~ c m}$. A chord of this circle is equal to the radius. Then the length of the arc of this chord is:

Equation of a circle whose area is 154 sq units and having $2 x-3 y+12=0$ and $x+4 y-5=0$ as diameters is

The equation of a circle passing through the origin is \(x^2+y^2-6 x+2 y=0\). The equation of one of its diameter is

The area (in sq units) of the minor segment bounded by the circle \(x^2+y^2=a^2\) and the line \(x=\frac{a}{\sqrt{2}}\) is

The equation of the circle which touches the \(x\)-axis, passes through the point \((1,1)\) and whose centre lies on the line \(x+y=3\) in the first quadrant is

The centre of the circle passing through \((0,0)\) and \((1,0)\) and touching the circle \(x^2+y^2=9\) is

\(S \equiv x^2+y^2-2 x-4 y-4=0\) and \(S^{\prime} \equiv x^2+y^2-4 x-2 y-16=0\) are two circles the point \((-2,-1)\) lies

The circle \(x^2+y^2+3 x-y+2=0\) cuts an intercept on \(X\)-axis of length

The points of intersection of circles \((x+1)^2+y^2=4\) and \((x-1)^2+y^2=9\) are \((a, \pm b)\), then \((a, b)\) equals to

\(S\equiv x^2+y^2+2x+3y+1=0\) and \(S'\equiv x^2+y^2+4x+3y+2=0\) are two circles. The point \((-3,-2)\) lies

the circle \({x^2} + {y^2} + 4x - 7y + 12 = 0\) cuts an intercept on Y-axis of length

If two circles \({(x - 1)^2} + {(y - 3)^2} = {r^2}\) and \({x^2} + {y^2} - 8x + 2y + 8 = 0\) intersect in two distinct points, then

What will be the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6)?

Find the centre and radius of the circle given by the equation \(2{x^2} + 2{y^2} + 3x + 4y + {9 \over 8} = 0\).

What will be the equation of circle whose centre is (1, 2) and touches X-axis?

If the circles \({x^2} + {y^2} - 2x - 2y - 7 = 0\) and \({x^2} + {y^2} + 4x + 2y + k = 0\) cut orthogonally, then the length of the common chord of the circles is

\({x^2} + {y^2} - 6x - 6y + 4 = 0\), \({x^2} + {y^2} - 2x - 4y + 3 = 0\), \({x^2} + {y^2} + 2kx + 2y + 1 = 0\). If the radical centre of the above three circles exists, then which of the following cannot be the value of k?

The equation to two circles which touch the
Y-axis at (0, 3) and make an intercept of 8 units
on X-axis are

If \(3x+y+k=0\) is a tangent to the circle \(x^2+y^2=10\), the values of k are

The number of common tangents to the circles \(x^2+y^2=4\) and \(x^2+y^2-6x-8y-24=0\) is,