List of top Mathematics Questions on general equation of a line asked in AP EAMCET

The angle between the line with the direction ratios \( (2, 5, 1) \) and the plane \( 8x + 2y - z = 4 \) is given by
If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then \( (\alpha, \beta) \) is:
The equation of the straight line passing through the point of intersection of the lines represented by \(x^2 + 4xy + 3y^2 - 4x - 10y + 3 = 0\) and the point \((2,2)\) is:
If \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) are position vectors of 4 points such that \( 2\vec{a} + 3\vec{b} + 5\vec{c} - 10\vec{d} = 0 \), then the ratio in which the line joining \( \vec{c} \) divides the line segment joining \( \vec{a} \) and \( \vec{b} \) is:
Equation of a tangent line of the parabola \(y^2 = 8x\), which passes through the point \((1, 3)\) is:
The algebraic equation of degree 4 whose roots are the translates of the roots of the equation \( x^4 + 5x^3 + 6x^2 + 7x + 9 = 0 \) by \( -1 \) is:
Let \( \alpha \in \mathbb{R} \). If the line \( (a + 1)x + \alpha y + \alpha = 1 \) passes through a fixed point \( (h, k) \) for all \( a \), then \( h^2 + k^2 = \):
If \( L_1 \) and \( L_2 \) are two lines which pass through origin and have direction ratios \( (3, 1, -5) \) and \( (2, 3, -1) \) respectively, then the equation of the plane containing \( L_1 \) and \( L_2 \) is:
The real values of \( x \) that satisfy the equation \[ \tan^{-1}x + \tan^{-1}2x = \frac{\pi}{4} \] is:
If the roots of the equation \( 4x^3 - 12x^2 + 11x + m = 0 \) are in arithmetic progression, then \( m = {?} \)
Roots of the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) are:
The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point \( (1,6) \) is:
If each line of a pair of lines passing through origin is at a perpendicular distance of $4$ units from the point $(3, 4)$, then the equation of the pair of lines is
In a $\Delta ABC, 2x + 3y + 1 = 0 , x + 2y - 2 = 0 $ are the perpendicular bisectors of its sides $AB$ and $AC$ respectively and if $A = (3,2)$, then the equation of the side $BC$ is