List of top Mathematics Questions on circle asked in KEAM

The centre and radius of the circle $x^2 + y^2 - 2x + 4y = 8$ respectively are:
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
Find \( \alpha \) if \[ \lim_{x \to 0} \frac{1 - \sec^2(\alpha x)}{\alpha x^2} = -3 \]
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 one end of a diameter of the circle \( x^2 + y^2 - 4x - 6y + 11 = 0 \) is \( (3, 4) \), then the coordinate of the other end of the diameter is:
Find the area of the smaller segment cut-off from the circle \( x^2 + y^2 = 25 \) by \( x = 3 \):
If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
The radius of the circle \( x^2 + y^2 - 2x - 4y - 4 = 0 \) is:
The equation of the circle whose radius is $\sqrt{7}$ and concentric with the circle $x^{2}+y^{2}-8x+6y-11=0$ is
A circle with centre at (3, 6) passes through (-1,1). Its equation is
The centre and radius of the circle $x^{2}+y^{2}-4x+2y=0$ are
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 \( (4,5) \)