List of top Questions asked in TS EAMCET

The value of 'a' for which the equation \((a^2-3)x^2 + 16xy - 2ay^2 + 4x - 8y - 2 = 0\) represents a pair of perpendicular lines is
A line L perpendicular to the line \( 5x-12y+6=0 \) makes positive intercept on the Y-axis. If the distance from the origin to the line L is 2 units and the angle made by the perpendicular drawn from the origin to the line L with positive X-axis is \( \theta \), then \( \tan \theta + \cot \theta = \)
O(0,0,0), A(3,1,4), B(1,3,2) and C(0,4,-2) are the vertices of a tetrahedron. If G is the centroid of the tetrahedron and \(G_1\) is the centroid of its face ABC, then the point which divides \(GG_1\) in the ratio 1:2 is
If (-1,-1) is the point of intersection of the pair of lines \(2x^2+5xy-3y^2+2gx+2fy+c=0\) then g+f=
If the points \((1, 1, \lambda)\) and \((-3, 0, 1)\) are equidistant from the plane \(3x + 4y - 12z + 13 = 0\), then the values of \(\lambda\) are
A circle C touches the X-axis and makes an intercept of length 2 units on the Y-axis. If the centre of this circle lies on the line $y=x+1$, then a circle passing through the centre of the circle C is
If the equation of the circumcircle of the triangle formed by the lines $L_1=x+y=0$, $L_2=2x+y-1=0$, $L_3=x-3y+2=0$ is $\lambda_1 L_2 L_3 + \lambda_2 L_3 L_1 + \lambda_3 L_1 L_2 = 0$, then $\frac{7\lambda_1+\lambda_3}{\lambda_2} =$
If A = (0,1), B = (1,2), C = (-2,1) then the equation of the locus of a point P such that area of triangle PAB = area of triangle PAC is
If the latus rectum through one of the foci of a hyperbola \( \frac{x^2}{9} - \frac{y^2}{b^2} = 1 \) subtends a right angle at the farther vertex of the hyperbola, then \(b^2 = \)
The curve represented by \(\frac{x^2}{12-\alpha} + \frac{y^2}{\alpha-10} = 1\) is
$y-x=0$ is the equation of a side of a triangle ABC. The orthocentre and circumcentre of the triangle ABC are respectively (5,8) and (2,3). The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then the radius of the circumcircle of the triangle is
Two non parallel sides of a rhombus are parallel to the lines $x+y-1=0$ and $7x-y-5=0$. If (1,3) is the centre of the rhombus and one of its vertices $A(\alpha, \beta)$ lies on $15x-5y=6$, then one of the possible values of $(\alpha+\beta)$ is
If $2x^2+xy-6y^2+k=0$ is the transformed equation of $2x^2+xy-6y^2-13x+9y+15=0$ when the origin is shifted to the point $(a,b)$ by translation of axes, then k =
If $P(\frac{7}{5}, \frac{6}{5})$ is the inverse point of $A(1,2)$ with respect to a circle with centre $C(2,0)$, then the radius of that circle is
A straight line through the point P(1,2) makes an angle $\theta$ with the positive X-axis in anti-clockwise direction and meets the line $x+\sqrt{3}y-2\sqrt{3}=0$ at Q. If $PQ = \frac{1}{2}$, then $\theta=$
If any tangent drawn to the ellipse \(\frac{x^2}{16} + \frac{y^2}{9} = 1\) touches one of the circles \(x^2 + y^2 = \alpha^2\), then the range of \(\alpha\) is
If the circle $S=0$ intersect the three circles $S_1 = x^2+y^2+4x-7=0$, $S_2 = x^2+y^2+y=0$ and $S_3 = x^2+y^2+\frac{3}{2}x+\frac{5}{2}y-\frac{9}{2}=0$ orthogonally, then the radical axis of $S=0$ and $S_1=0$ is
A circle S given by \(x^2 + y^2 - 14x + 6y + 33 = 0\) cuts the X-axis at A and B (OB \(>\) OA). C is midpoint of AB. L is a line through C and having slope \((-1)\). If L is the diameter of a circle S' and also the radical axis of the circles S and S', then the equation of the circle S' is
If S and S' are the foci of an ellipse \( \frac{x^2}{169} + \frac{y^2}{144} = 1 \) and the point B lying on positive Y-axis is one end of its minor axis, then the incentre of the triangle SBS' is
The angle between the tangents drawn from the point P(k, 6k) to the circle \(x^2+y^2+6x-6y+2=0\) is \(2\tan^{-1}(\frac{4}{3})\). If the coordinates of P are integers, then k =
A normal chord PQ drawn at a point P on the parabola \(y^2=5x\) subtends a right angle at the vertex. If P lies in the first quadrant, then the other end Q of the normal chord is
A line segment joining a point A on x-axis to a point B on y-axis is such that AB = 15. If P is a point on AB such that \(\frac{AP}{PB} = \frac{2}{3}\), then the locus of P is
If a tangent to the circle $x^2+y^2+2x+2y+1=0$ is radical axis of the circles $x^2+y^2+2gx+2fy+c=0$ and $2x^2+2y^2+3x+8y+2c=0$, then
If $\text{Tan}^{-1}(2\sqrt{10})$ is the angle between the lines $ax^2+4xy-2y^2=0$ and $a \in \mathbb{Z}$, then the product of the slopes of given lines is
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