List of top Mathematics Questions on Straight lines asked in KEAM

The straight line passing through the points $(1, 5)$ and $(3, -5)$ meets the coordinate axes at the points $A$ and $B$. Then the area of the triangle $\triangle OAB$, where $O$ is the origin, is
If the equation of the straight line passing through the points $(3, -4)$ and $(4, a)$ is $x - y = 7$, then the value of $a$ is equal to
A point C lies on the perpendicular bisector of the straight-line segment joining the points A(-3,-6) and B(13,-6). If the point C lies in the first quadrant and the distance between the point C and the midpoint of AB is 8 units, then the coordinates of C are
Let A(-4,3), B(0,5) and C(-1,2) be three points. The equation of the straight line which passes through C and bisects the straight-line segment AB is
If the points $(3,-2)$, $(a,2)$, $(8,8)$ are collinear, then the value of $a$ is:
The distance of the point $P(1,-3)$ from the line $2y - 3x = 4$ is:
If the foot of the perpendicular drawn from the origin to the line $y=mx+c$ is $(1,1)$ then the value of $m$ and $c$ are, respectively,
The x-intercept and y-intercept of a line are three times and four times of the x-intercept and y-intercept of the line $3x+2y=6$, respectively. Then the equation of the line is
The perpendicular drawn from the origin to the straight line $\sqrt{3}x + y - 24 = 0$ makes an angle $\alpha$ with the positive direction of x-axis. Then $\alpha$ is equal to:
A straight line makes $y$-intercept of 5. If the angle made by the line with $y$-axis is $60^\circ$ and the line intersects $x$-axis in the negative direction, then the equation of the line is
The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is
Let $a \ne 1$ be a non-zero real number. If the lines $2x+ay=1$ and $x+2y=1$ are perpendicular, then the value of $a$ is equal to ________.
If the normal form of the equation of a straight line \( x+\sqrt{3}y=2\sqrt{3} \) is \( x\cos\alpha+y\sin\alpha=p \), then the values of \( \alpha \) and \( p \) are respectively
The point with integral coordinates on the line \(x+y=1\), that lie at a distance \(2\) units from the line \(5x+12y=0\), is
If the line joining of two points \((1,0)\) and \((4,3)\) is rotated about the point \((1,0)\) in counter clockwise direction through an angle \(15^\circ\), then the equation of the line in the new position is
Let $ax+by+c=0$ be the equation of a straight line such that $3a+2b+4c=0$. Which one of the following points lies on the line?
Two sides of a parallelogram are along the lines $x+y=5$ and $x-y=-5.$ If the diagonals of the parallelogram intersect at (3, 6) then one of its vertices is at
If the distance of the line $4x-3y+k=0$ from the point (1, 2) is 5 units, then the values of k are
The straight line \( ax + by + c = 0 \) passes through the point \( (-10,7) \). If the line is perpendicular to \( 11x - 7y = 13 \), then the value of \( c \) is equal to
Let $A(-1,\,2)$, $B(1,\,-2)$ and $C(-2,\,-2)$ be vertices of the triangle $ABC$. The equation of the line passing through $C$ and parallel to $AB$ is
If the straight lines \( \frac{x - 3}{2} = \frac{y - 4}{3} = \frac{z - 6}{-1} \) and \( \frac{x - 2}{a} = \frac{y + 3}{b} = \frac{z + 4}{-1} \) are parallel, then \( a^2 + b^2 \) is:
\[ \cos^{-1} \left( \cos \left( \frac{-7\pi}{9} \right) \right) = \]

\[ \int \left( \frac{\log_e t}{1+t} + \frac{\log_e t}{t(1+t)} \right) dt \]

If \( \left( 1 + \cos \frac{\pi}{8} \right) \left( 1 + \cos \frac{7\pi}{8} \right) \) =
Suppose the point \(P(1,1)\) is translated to \(Q\) in the direction of y = 2x. If \(PQ = 1\),then Qis