List of top Mathematics Questions on Straight lines asked in MET

\(\int \sqrt{1 + \csc x} dx\) is equal to

If \(\int \frac{dx}{x^2(x^n + 1)^{(n-1)/n}} = -[f(x)]^{1/n} + c\) then \(f(x)\) is

One diagonal of a square is along the line \( 8x - 15y = 0 \) and one of its vertices is \( (1, 2) \). Then, the equation of the sides of the square passing through this vertex are

The circumcenter of a triangle formed by the lines \( xy + 2x + 2y + 4 = 0 \) and \( x + y + 2 = 0 \) is

The ratio in which the line \( 3x + 4y + 2 = 0 \) divides the distance between \( 3x + 4y + 5 = 0 \) and \( 3x + 4y - 5 = 0 \) is

The line \( x + 2y = 4 \) is translated parallel to itself by 3 units in the sense of increasing \( x \) and then rotated by 30° in the anti-clockwise direction about the point where the shifted line cuts the x-axis. The equation of the line in the new position is:

If the equation \( 12x^2 + 7xy - py^2 - 18x + qy + 6 = 0 \) represents a pair of perpendicular straight lines, then

The equation of the straight line which passes through the intersection of the lines $x-y-1=0$ and $2x-3y+1=0$ and is parallel to x-axis, is

The distance of the point (2, 3) from the line $2x-3y+9=0$ measured along a line $x-y+1=0$ is

The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

The point on the line $3x+4y=5$ which is equidistant from $(1, 2)$ and $(3, 4)$ is

The equation of the straight line perpendicular to the straight line $3x+2y=0$ and passing through the point of intersection of the lines $x+3y-1=0$ and $x-2y+4=0$ is

The value of \( \lambda \) with \( |\lambda| < 16 \) such that \( 2x^2 - 10xy + 12y^2 + 5x + \lambda y - 3 = 0 \) represents a pair of straight lines, is

The area (in square unit) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is

The orthocentre of the triangle formed by the axes and the line $x + y = 1$ is:

The orthocentre of the triangle formed by the axes and the line $x + y = 1$ is:

The length of the perpendicular from the origin to the line $3x+4y-10=0$ is:

The area of the triangle with vertices $(1, 2), (3, 4)$ and $(5, 2)$ is:

The distance between the parallel lines $y = x + 4$ and $y = x - 2$ is:

The equation of the line passing through the point $(1, 2)$ and perpendicular to the line $x + y + 1 = 0$ is: