List of top Mathematics Questions asked in TS EAMCET

Let \(ABC\) be a triangle and \(A=(-2,3)\). If \[ 7x-y+2=0 \] and \[ 4x-7y+44=0 \] are medians drawn through vertices B and C respectively, then \(AB=\)

Let \(L=0\) be the chord of contact of \((5,1)\) with respect to the circle \[ S\equiv x^2+y^2+8x+10y-8=0. \] If the pole of \(L=0\) with respect to the circle \[ S'\equiv x^2+y^2+4y-21=0 \] is \((-k,-h)\), then \(k+h=\)

Let \(A(1,1)\) and \(B(-1,-1)\) be the points of contact of tangents drawn from a point \(P\) to the circle \(x^2+y^2-2x+2y-2=0\). If \(C\) is the centre of the circle, then the centre of the circle passing through \(A,B,C,P\) is

When origin is shifted to point \[ \left(-\frac47,\frac67\right) \] and transformed equation of \[ 2x^2+5xy+4y^2-2x-4y+2=0 \] is \[ ax^2+35xy+by^2+2gx+2fy+c=0 \] then

If circle \[ x^2+y^2+2x+4y+k=0 \] lies totally inside third quadrant and point \[ \left(-\frac12,-\frac12\right) \] lies outside circle, then set of all real values of \(k\) is

When axes are rotated through an angle \(\theta\) about the origin in the positive direction, if the equation \[ 3x^2+\sqrt{3}xy-5=0 \] is transformed to the form \[ ax'^2+by'^2=10, \] then \(ab=\)

Let P be a variable point such that it forms a triangle of area 14 square units with two fixed points \((-3,4)\) and \((4,-3)\). Then the locus of P represents a pair of parallel lines. The distance between these two parallel lines is

The distance between the internal and external centres of similitude with respect to the circles \[ x^2+y^2+4x+6y+12=0 \] and \[ x^2+y^2-6x-4y+9=0 \] is:

Let P be any point on circle \(x^2+y^2=16\) and \(A=(1,2)\). If the locus of point dividing AP in ratio 3:2 is a circle, its radius is:

The line \((3a+1)x+(7a+2)y=17a+5\) represents concurrent lines. If \(d\) is distance from \((3,1)\) to line of slope 1 in this family, find \(2d^2\):

If the circles \[ x^2+y^2-10x+8y+5=0 \] and \[ x^2+y^2+6x-4y+c=0 \] cut each other orthogonally, then the sum of the radii of these circles is

Orthocentre of triangle formed by pair of lines \[ 2x^2-xy-3y^2=0 \] and line \[ x-y+4=0 \] is

If the major axis of an ellipse is parallel to the \(X\)-axis and the ratio of the lengths of its latus rectum and minor axis is \(2:3\), then the ratio of distances from its centre to its focus and directrix is

If the length of a focal chord drawn to the parabola \[ y^2=64x \] is \(289\) and the angle made by this focal chord with the positive \(X\)-axis measured in the positive direction is an acute angle, then the slope of the focal chord is

The parametric equation of a circle passing through origin are given by \[ x=-g+5\cos\theta, \qquad y=-f+5\sin\theta. \] If the straight line passing through origin with slope \[ -\frac43 \] is the diameter of this circle, then the sum of the intercepts made by this circle on the coordinate axes is

If \(3x+4y-24=0\) and \(3x-4y-32=0\) are tangents to a circle and \(4x+3y-1=0\) is a normal, then \(r+h+k=\):

If the inclination of a straight line \[ x-y+1=0 \] with another straight line \(L\) is \(30^\circ\) and \(m\) is the slope of line \(L\), then \[ m^2+1= \]

If the equation of the line joining the points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \[ ax+by=c \] and the distance between \(A\) and \(B\) is \(\sqrt{a^2+b^2}\), then \(c^2=\)

If a straight line passing through the point \((2,3)\) intersects X-axis at A and Y-axis at B, then the locus of a point dividing AB in the ratio \(2:3\) is

The tangent drawn at a point \(P\) on the circle \(x^{2}+y^{2}+6x+6y-2=0\) cuts the line \(5x-2y+6=0\) at a point \(Q\). If \(PQ=5\), then a point \(Q\) having integral coordinates is:

The length of the common chord of the circles \[ x^2+y^2-8x-6y-11=0 \] and \[ x^2+y^2-6x+8y+9=0 \] is

If \(d\) is the distance of a point \(P(-1,2)\) to the line \(x+2y-4=0\) measured along a straight line which is parallel to the straight line \(x-\sqrt{3}y+5=0\), then \(d=\)

The transformed equation of \[ 4x^2-4xy+7y^2-24=0 \] in the new coordinate system when the axes are rotated through an angle \(\theta\) about the origin in the positive direction is \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1. \] If \[ 0<\theta<\frac{\pi}{4}, \] then \[ 1+b^2\sin^2\theta= \]

Two straight lines are drawn parallel to the straight line \[ L\equiv 5x-12y-13=0 \] which are at a distance of \(13\) units from the given line. Among these lines, if \[ ax+by+c=0 \] is the line which is closest to \[ L=0, \] then \[ \frac{a-2b+c}{a+b} = \]

A straight line passes through a point \(A(2,5)\) and makes an angle of \(45^\circ\) with the positive X-axis when measured in positive direction. If this line intersects the line passing through the points \((1,-2)\) and \((3,-4)\) at \(B\), then \(AB=\)