List of top Mathematics Questions on Coordinate Geometry asked in TS EAMCET

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

If a circle inscribed in the parabola \(y^{2}=4ax\) passes through its focus, then the equation of the circle 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:

If line \(4x-3y+c=0\) makes a chord of length 10 on circle \(x^2+y^2-2x+4y-23=0\), then \(c=\):

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

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:

If two vertices of a quadrilateral are the centres of the circles \[ S\equiv x^{2}+y^{2}-2x-2y-2=0 \] and \[ S^{\prime}\equiv x^{2}+y^{2}-6x-6y+14=0 \] and the other two vertices of that quadrilateral are the points of intersection of these two circles, then the area of the quadrilateral is:

If the coordinate axes are rotated about the origin through \(60^\circ\), the equation \(x^{2}+y^{2}-4x-8y+16=0\) becomes \(x^{2}+y^{2}+2Gx+2Fy+C=0\). Then \(G+F+C=\):

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 \(2d^2\):

A ray from (7,2) reflects on \(2x+y=1\) and passes through (3,10). Equation of incident ray is:

In triangle ABC, B lies on positive x-axis, A=(-1,0), \(a=4\sqrt{3}\), \(\angle A=120^\circ\). If C has integer coordinate condition, distance of C from origin is:

One of the pair of lines \(x^{2}-3y^{2}-4x-6\sqrt{3}y-5=0\) is \(x+by+c=0\) \((b<0)\). If the other line intersects the curve \(x^{2}-5y^{2}-4x=0\) at two points A and B, then \(\angle AOB=\):

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:

If the circles \[ x^2+y^2+2gx+6y+4=0 \] and \[ x^2+y^2-gx-2y-14=0 \] cut each other orthogonally for a positive integral value of \(g\), then the radical axis of the two circles is:

If the equation \[ x+2y=3 \] represents the chord \(AB\) of the circle \[ x^2+y^2-4y=0, \] then the equation of the circle with \(AB\) as diameter 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 \(d=\)

A ray of light \(x+y=1\) gets reflected upon the X-axis. If the reflected ray forms a triangle with X-axis and the vertical line \(x=2\), then the area of that triangle is

The centroid of the triangle formed by the lines \(6x^2+xy-2y^2=0\) and \(x+2y+3=0\) is

A circle \(S\equiv x^2+y^2+4x+2fy+c=0\) passes through the centre of the circle \(x^2+y^2-4x+6y-2=0\). If the line \(3x-3y=c\) passes through the centre of the circle \(S=0\), then the length of tangent from \((1,1)\) to the circle \(S=0\) is

Let \(P=(0,2)\). Let \(A(x_1,y_1)\) and \(B(x_2,y_2)\) be two points on the circle \(x^2+y^2-6x+4y+4=0\) such that \(PA\) is minimum and \(PB\) is maximum. Then \(\frac{3(y_1-y_2){(x_2-x_1)}=\)}

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

If \((h,k)\) is the point to which the origin has to be shifted by translation of axes to remove the terms containing \(x\) and \(y\) from the equation \[ 2x^2+3xy+y^2+4x-8y+5=0 \] then \(2h+k=\)

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 \(AB=\)

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

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 \(AB=\)