List of top Questions asked in AP EAPCET- 2025

If the combined equation of the lines joining the origin to the points of intersection of the curve $ x^2 + y^2 - 2x - 4y + 2 = 0 $ and the line $ x + y - 2 = 0 $ is $ (l_1x + m_1y)(l_2x + m_2y) = 0 $, then $ l_1 + l_2 + m_1 + m_2 = $
The point P(4, 1) undergoes the following transformations in succession: (i) origin is shifted to the point (1, 6) by translation of axes, (ii) translation through a distance of 2 units along the positive direction of the x-axis, (iii) rotation of axes through an angle of $90^\circ$ in the positive direction. Then the coordinates of the point P in its final position are
If the radical axis of the circles $x^2+y^2+2gx+2fy+c=0$ and $2x^2 + 2y^2 + 3x + 8y + 2c = 0$ touches the circle $x^2 + y^2 + 2x + 2y + 1 = 0$, then
If the tangent drawn at the point \((\alpha, \beta)\) on the curve \[ x^{2/3} + y^{2/3} = 4 \] is parallel to the line \[ \sqrt{3}x + y = 1, \] then \( \alpha^2 + \beta^2 =\)
$3x+4y-43=0$ is a tangent to the circle $S = x^2+y^2-6x+8y+k=0$ at a point P. If C is the center of the circle and Q is a point which divides CP in the ratio -1:2, then the power of the point Q with respect to the circle S=0 is
If \( Q \) is the inverse point of \( P(-1, 1) \) with respect to the circle \( x^2 + y^2 - 2x + 2y = 0 \), then the line containing \( Q \) is:
If the angle between the pair of lines $2x^2 + 2hxy + 2y^2 - x + y - 1 = 0$ is $\tan^{-1}\left(\frac{3}{4}\right)$ and $h$ is a positive rational number, then the point of intersection of these two lines is
A circle touches the x-axis at point \( (4,0) \) and its center lies on the line \( x + y = 6 \). What is the equation of the circle?
If the lines \( x + 2ay + a = 0 \), \( x + 3by + b = 0 \), \( x + 4cy + c = 0 \) are concurrent, then \( a, b, c \) are in
If \( M \) is the foot of the perpendicular drawn from the origin to the line \( x - 2y + 3 = 0 \), which meets the X and Y-axes at \( A \) and \( B \) respectively, then \( AM = \)
If \( A(0,0,0),\ B(3,4,0),\ C(0,12,5) \) are the vertices of a triangle ABC, then the x-coordinate of its incenter is:
If the equation of the pair of straight lines intersecting at $ (a, b) $ and perpendicular to the pair $$ 3x^2 - 4xy + 5y^2 = 0 $$ is $$ lx^2 + 2hxy + my^2 = 0, $$ then find $$ \frac{a + b + c}{l + h + m}. $$
A$(-2, 3)$ is a point on the line $4x + 3y - 1 = 0$. If the points on the line that are 10 units away from the point A are $(x_1, y_1)$ and $(x_2, y_2)$, then $(x_1 + y_1)^2 + (x_2 + y_2)^2 =\ ?$
If a tangent to the hyperbola \( xy = -1 \) is also a tangent to the parabola \( y^2 = 8x \), then the equation of that tangent is:
If the equation of the circle passing through the point $(8, 8)$ and having the lines $x + 2y - 2 = 0$ and $2x + 3y - 1 = 0$ as its diameters is $x^2 + y^2 + px + qy + r = 0$, then $p^2 + q^2 + r =$
One line of the pair of lines \( x^2 + xy - 2y^2 = 0 \) is perpendicular to one line of the pair of lines \( 3y^2 - 5xy - 2x^2 = 0 \). If the combined equation of the two lines other than those two perpendicular lines is \( ax^2 + 2hxy + by^2 = 0 \), then \( a + 2h + b = \)
A straight line passing through a fixed point (2, 3) intersects the coordinate axes at points \( P \) and \( Q \). If \( O \) is the origin and \( R \) is a variable point such that \( OPRQ \) is a rectangle, then the locus of \( R \) is
$L_1 = ax - 3y + 5 = 0$ and $L_2 = 4x - 6y + 8 = 0$ are two parallel lines. If $p, q$ are the intercepts made by $L_1 = 0$ and $m, n$ are the intercepts made by $L_2 = 0$ on the X and Y coordinate axes, respectively, then the equation of the line passing through the points $(p, q)$ and $(m, n)$ is
By rotating the axes about the origin in anti-clockwise direction with certain angle, if the equation \( x^2 + 4xy + y^2 = 1 \) is transformed to \( \frac{x'^2}{a^2} - \frac{y'^2}{b^2} = 1 \), then \( \sqrt{\frac{a^2 + b^2}{a^2}} = \)
PQ is a focal chord of the parabola \( y^2 = 4x \) with focus S. If \( P = (4,4) \), then SQ = ?
A circle \( S = x^2 + y^2 - 16 = 0 \) intersects another circle \( S' = 0 \) of radius 5 units such that their common chord is of maximum length. If the slope of that chord is \( \dfrac{3}{4} \), then the centre of such a circle \( S' = 0 \) is:
If a unit circle $S = x^2 + y^2 + 2gx + 2fy + c = 0$ touches the circle $S' = x^2 + y^2 - 6x + 6y + 2 = 0$ externally at the point $(-1, -3)$, then $g + f + c =$
The distance between the tangents of the hyperbola \( 2x^2 - 3y^2 = 6 \) which are perpendicular to the line \( x - 2y + 5 = 0 \) is:
If the incentre of the triangle formed by lines $$ x - 2 = 0, \quad x + y - 1 = 0, \quad x - y + 3 = 0 $$ is $ (\alpha, \beta) $, then find $ \beta $.
A plane \( \pi \) is passing through the points \( A(1, -2, 3) \) and \( B(6, 4, 5) \). If the plane \( \pi \) is perpendicular to the plane \( 3x - y + z = 2 \), then the perpendicular distance from \( (0, 0, 0) \) to the plane \( \pi \) is