List of top Questions asked in AP EAPCET- 2026

If the equation of a circle passing through the point (2, 1) and the points of intersection of the circles $x^{2}+y^{2}+4x-6y-3=0$ and $x^{2}+y^{2}-2x+2y-2=0$ is $x^{2}+y^{2}+2gx+2fy+c=0$, then $2g+f=$

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

The locus of the centre of a circle of radius 2 which rolls on the outside of the circle \( x^{2}+y^{2}+3x-6y-9=0 \) along its circumference is

Find the interval of \(\lambda\) for which exactly two common tangents can be drawn to \(x^2+y^2-4x-4y+6=0\) and \(x^2+y^2-10x-10y+\lambda=0\).

A circle C cuts the circles \(x^{2}+y^{2}-4x+6y+4=0\) and \(x^{2}+y^{2}+6x-4y+9=0\) orthogonally. If origin lies on this circle C, then the radius of the circle C is

The equation of the circle passing through the points of intersection of the circles \[ x^2+y^2-2x-4y+1=0, \] \[ x^2+y^2-4x-2y+4=0 \] and having its centre on the line \[ x-2y-3=0 \] is

If the centre of a circle \(S\) is \((2,4)\) and the length of the chord made by the secant \[ x+y+2=0 \] on \(S\) is \(6\) units, then the equation of the circle \(S\) 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:

Equation of the circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length \(3\) 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:

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

If the points \[ (2,0),\ (0,1),\ (4,0),\ (0,k) \] are concyclic, then \(k=\)

The point of intersection of the lines \[ 2x+3y-12=0 \] and \[ 3x-2y-5=0 \] is the centre of a circle \(S=0\). If \(AB\) is a chord of \(S=0\) and it is a diameter of the circle \[ x^2+y^2-10x+4y+13=0, \] then the radius of the circle \(S=0\) is

If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ passes through the origin, has radius 3, and its center lies on the line $x + y = 4$, then $g + f =$

If a tangent drawn to the circle $x^{2}+y^{2}-6x-8y-11=0$ is perpendicular to the line $3x + 4y + k = 0$, then the distance from the origin to this tangent is

The centre of the circle which intersects the circles \[ x^2+y^2-8x+10y+5=0 \] and \[ x^2+y^2-2x+2y+1=0 \] orthogonally is:

If the chord \(y=mx+1\) of the circle \(x^2+y^2=1\) subtends an angle \(45^\circ\) at the major segment of the circle, then the value of \(m\) is:

The equation of the line that is a tangent to the circle \[ x^2+y^2-6x+4y+12=0 \] is

The tangent to the circle \(C_1:x^2+y^2-2x-1=0\) at the point \((2,1)\) cuts off a chord of length \(4\) units from a circle \(C_2\) whose centre is \((3,-2)\). The radius of circle \(C_2\) 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 \( 2x+y-2=0 \) and \( 6x-4y+1=0 \) are two normals of a circle S and the length of the perpendicular drawn from (2, 3) to the line \( 3x+4y-3=0 \) is the radius of S, then the interior point of the circle S among the following options is

Let \( \theta \) be the angle between the circles \( x^{2}+y^{2}-4x+2fy-f=0 \) and \( x^{2}+y^{2}+2fx-4y-f=0 \). If \( \cos\theta=\frac{9}{16} \) and \( f\in\mathbb{Z} \), then the distance between the centres of these circles is

The perpendicular distance from origin to the tangent drawn at the point \( P(\frac{\pi}{4}) \) to the circle \( x^{2}+y^{2}-4x-4y+6=0 \) is

A variable circle passes through the fixed point \(A(p,q)\) and touches the X-axis. The locus of the other end of the diameter through A is