List of top Mathematics Questions on Straight lines asked in KEAM

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
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
The image of the point $P(2,1)$ on the straight line $2x - 3y + 1 = 0$ is
If \( \theta \) is the angle between the pair of straight lines \( x^2 - 5xy + 4y^2 + 3x - 4 = 0 \), then \( \tan^2\theta \) is equal to
If \( x^2 + y^2 + 2gx + 2fy + 1 = 0 \) represents a pair of straight lines, then \( f^2 + g^2 \) is equal to
Equation of line through \( (a,b) \) parallel to \( \frac{x}{a} + \frac{y}{b} = 1 \)
Equation of line through \( (a,b) \) parallel to \( \frac{x}{a} + \frac{y}{b} = 1 \)
If \( x^2 + y^2 + 2gx + 2fy + 1 = 0 \) represents a pair of straight lines, then \( f^2 + g^2 \) is equal to
If \( \theta \) is the angle between the pair of straight lines \( x^2 - 5xy + 4y^2 + 3x - 4 = 0 \), then \( \tan^2\theta \) is equal to
If \( x^2 + y^2 + 2gx + 2fy + 1 = 0 \) represents a pair of straight lines, then \( f^2 + g^2 \) is equal to
If \( \theta \) is the angle between the pair of straight lines \( x^2 - 5xy + 4y^2 + 3x - 4 = 0 \), then \( \tan^2\theta \) is equal to
Equation of line through \( (a,b) \) parallel to \( \frac{x}{a} + \frac{y}{b} = 1 \)
The distance of the point \( (3, -5) \) from the line \( 3x - 4y - 26 = 0 \) is:
The equation of the line passing through \( (-3, 5) \) and perpendicular to the line through the points \( (1, 0) \) and \( (-4, 1) \) is: