List of top Mathematics Questions on circle asked in KEAM

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
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 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
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
If the circles \( x^2+y^2-8x-6y+c=0 \) and \( x^2+y^2-2y+d=0 \) cut orthogonally, then \( c+d \) equals
If the centre of the circle inscribed in a square formed by the lines $x^2 - 8x + 12 = 0$ and $y^2 - 14y + 45 = 0$ is $(a,b)$, then $a + b$ is
The circle passing through \( (1, -2) \) 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:
Equation of circle with centre \( (2,2) \) passing through \( (4,5) \)
Equation of circle with centre \( (2,2) \) passing through \( (4,5) \)
The area of the circle \( x^2 - 2x + y^2 - 10y + k = 0 \) is \( 25\pi \). The value of \( k \) is equal to:
If the area of the circle $4x^2 + 4y^2 + 8x - 16y + \lambda = 0$ is $9\pi$ sq. units, then the value of $\lambda$ is:
The radius of the circle passing through the points $(2,3)$, $(2,7)$ and $(5,3)$ is:
If a diameter of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord of another circle $C$ having centre $(2, 1)$, then the radius of the circle $C$ is:
In the family of concentric circles $2(x^2 + y^2) = k$, the radius of the circle passing through $(1, 1)$ is:
\(ABCD\) is a square with side \(a\). If \(AB\) and \(AD\) are along the coordinate axes, then the equation of the circle passing through the vertices \( A, B \) and \( D \) is
The point on the circle \( (x-1)^2 + (y-1)^2 = 1 \) which is nearest to the circle \( (x-5)^2 + (y-5)^2 = 4 \) is
The parametric form of equation of the circle \( x^2 + y^2 - 6x + 2y - 28 = 0 \) is
A circle passes through the point \( (6,2) \). If segments of the straight lines \( x+y=6 \) and \( x+2y=4 \) are two diameters of the circle, then its radius is