JEE MAIN Straight Line Previous Year Questions (PYQs) – Page 11 of 13

The region represented by $|x-y|\le 2$ and $|x+y|\le 2$ is bounded by a:

The point $(2,1)$ is translated parallel to the line $L : x - y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is:

If a variable line drawn through the intersection of the lines $\dfrac{x}{3} + \dfrac{y}{4} = 1$ and $\dfrac{x}{4} + \dfrac{y}{3} = 1$ meets the coordinate axes at $A$ and $B$ $(A \ne B)$, then the locus of the midpoint of $AB$ is:

Let a line passing through the point $(4,1,0)$ intersect the line $\mathrm{L}_1: \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ at the point $A(\alpha, \beta, \gamma)$ and the line $\mathrm{L}_2: x-6=y=-z+4$ at the point $B(a, b, c)$. Then $\left|\begin{array}{lll}1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c\end{array}\right|$ is equal to

Line $L_1$ passes through the point $(1, 2, 3)$ and is parallel to the $z$-axis. Line $L_2$ passes through the point $(\lambda, 5, 6)$ and is parallel to the $y$-axis. Let for $\lambda = \lambda_1, \lambda_2,$ $\lambda_2 < \lambda_1,$ the shortest distance between the two lines be $3$. Then the square of the distance of the point $(\lambda_1, \lambda_2, 7)$ from the line $L_1$ is

If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to –4, then a value of k is :

If the lines $x=ay+b,\ z=cy+d$ and $x=a'z+b',\ y=c'z+d'$ are perpendicular, then:

Let $\alpha_1, \alpha_2 ; (\alpha_1 < \alpha_2)$ be the values of $\alpha$ for the points $(\alpha, -3), (2, 0)$ and $(1, \alpha)$ to be collinear. Then the equation of the line, passing through $(\alpha_1, \alpha_2)$ and making an angle of $\frac{\pi}{3}$ with the positive direction of the x-axis, is :

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_1: 2x+y+6=0$ and $L_2: 4x+2y-p=0,; p>0$ at the points $A$ and $B$, respectively. If $|AB|=\dfrac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$, then $\dfrac{AM}{BM}$ is equal to

If the shortest distance between the straight lines $3(x - 1) = 6(y - 2) = 2(z - 1)$ and $4(x - 2) = 2(y - \lambda ) = (z - 3),\lambda \in R$ is ${1 \over {\sqrt {38} }}$, then the integral value of $\lambda$ is equal to :