List of top Mathematics Questions asked in AP EAPCET

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

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

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:

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

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

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

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

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

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:

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:

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

Two circles, each of radius 5, touch at $(1,2)$. If the common tangent at the point of contact is $4x+3y=10$, then the equation of one of the 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

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:

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

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

The external centre of similitude of the two circles \[ x^2+y^2-4x+6y+4=0 \] and \[ x^2+y^2-2x+2y-2=0 \] is

The radical axis of two orthogonal circles is \(x+1=0\). If one of those circles is \(x^2+y^2=4\), then the equation of the other circle 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

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 a circle passing through the points $(1, 5)$ and $(4,0)$ makes equal intercepts on coordinate axes and if its centre lies in the first quadrant, then $\sqrt{4g^{2}-c^{2}}=$

If $L$ represents a normal drawn at the point $P\left(\frac{\pi}{4}\right)$ on the circle $x^{2}+y^{2}+6x-6y-14=0$, then the equation of the diameter of this circle which is perpendicular to $L$ is

The line \( 5x-12y-4=0 \) cuts the circle \( x^{2}+y^{2}-2x+2y+c=0 \) at two points A, B. If \( AB=2\sqrt{3} \), then the length of the tangent drawn from the point (2, 1) to the given circle is