List of top Questions asked in AP EAMCET- 2024

If \( \theta \) is the angle between the tangents drawn from the point \( (2,3) \) to the circle \( x^2 + y^2 - 6x + 4y + 12 = 0 \), then \( \theta \) is:
If the axes are rotated through an angle \( \alpha \), then the number of values of \( \alpha \) such that the transformed equation of \( x^2 + y^2 + 2x + 2y - 5 = 0 \) contains no linear terms is:
If the slope of one of the lines in the pair of lines \( 8x^2 + axy + y^2 = 0 \) is thrice the slope of the second line, then \( a = \) ?
The equation of the locus of points that are equidistant from the points \( (2,3) \) and \( (4,5) \) is:
Angle between the circles \( x^2 + y^2 - 4x - 6y - 3 = 0 \) and \( x^2 + y^2 + 8x - 4y + 11 = 0 \) is:
If the straight line passing through \( P(3,4) \) makes an angle \( \frac{\pi}{6} \) with the positive x-axis in the anticlockwise direction and meets the line \( 12x + 5y + 10 = 0 \) at \( Q \), then the length of the segment \( PQ \) is:
If a man of height 1.8 m is walking away from the foot of a light pole of height 6 m with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph):
If \( Q(h, k) \) is the inverse point of \( P(1,2) \) with respect to the circle \( x^2 + y^2 - 4x + 1 = 0 \), then \( 2h + k \) is:
Suppose the axes are to be rotated through an angle \( \theta \) so as to remove the \( xy \) term from the equation \(3 x^2 + 2\sqrt{3}xy + y^2 = 0 \). Then in the new coordinate system, the equation \( x^2 + y^2 + 2xy = 2 \) is transformed to:
The locus of a variable point which forms a triangle of fixed area with two fixed points is:
The locus of the midpoint of the portion of the line \( x \cos \alpha + y \sin \alpha = p \) intercepted by the coordinate axes, where \( p \) is a constant, is:
Equation of the line touching both parabolas \( y^2 = 4x \) and \( x^2 = -32y \) is:
The line \( 21x + 5y = k \) touches the hyperbola \( 7x^2 - 5y^2 = 232 \), then \( k \) is:
If the distance between the planes \( 2x + y + z + 1 = 0 \) and \( 2x + y + z + \alpha = 0 \) is 3 units, then the product of all possible values of \( \alpha \) is:
If \( A(1,2,0), B(2,0,1), C(-3,0,2) \) are the vertices of \( \triangle ABC \), then the length of the internal bisector of \( \angle BAC \) is:
The origin is shifted to the point \( (2, 3) \) by translation of axes and then the coordinate axes are rotated about the origin through an angle \( \theta \) in the counter-clockwise sense. Due to this if the equation \( 3x^2 + 2xy + 3y^2 - 18x - 22y + 50 = 0 \) is transformed to \( 4x^2 + 2y^2 - 1 = 0 \), then the angle \( \theta = \):
The orthocentre of triangle formed by points: \( (2,1,5) \), \( (3,2,3) \) and \( (4,0,4) \) is:

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

If the circles \( S = x^2 + y^2 - 14x + 6y + 33 = 0 \) and \( S' = x^2 + y^2 - a^2 = 0 \) (where \( a \in \mathbb{N} \)) have 4 common tangents, then the possible number of values of \( a \) is: 
Parametric equations of the circle \( 2x^2 + 2y^2 = 9 \) are:
If \( (a, b) \) is the stationary point of the curve \( y = 2x - x^2 \), then the area bounded by the curves \( y = 2x - x^2 \), \( y = x^2 - 2x \), and \( x = a \) is:
The length of the tangent drawn from the point \( \left(\frac{k}{4}, \frac{k}{3}\right) \) to the circle \( x^2 + y^2 + 8x - 6y - 24 = 0 \) is:
Let \( P(a, 4, 7) \) and \( Q(3, \beta, 8) \) be two points. If the YZ-plane divides the join of the points P and Q in the ratio 2:3 and the ZX-plane divides the join of P and Q in the ratio 4:5, then the length of line segment PQ is:
The normal drawn at \( (1,1) \) to the circle \( x^2 + y^2 - 4x + 6y - 4 = 0 \) is:
Find the equation of a line passing through the intersection of \( 3x + y - 4 = 0 \) and \( x - y = 0 \), and making a \( 45^\circ \) angle with \( x - 3y + 5 = 0 \).