JEE MAIN Straight Line Previous Year Questions (PYQs) – Page 10 of 13
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If p and q are the lengths of the perpendiculars from the origin on the lines,:- x cosec $\alpha$ $-$ y sec $\alpha$ = k cot 2$\alpha$ and, x sin$\alpha$ + y cos$\alpha$ = k sin2$\alpha$ respectively, then k2 is equal to :
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Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$.
If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?
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The shortest distance, between lines $L_1$ and $L_2$, where $L_1: \frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}$ and $L_2$ is the line, passing through the points $\mathrm{A}(-4,4,3), \mathrm{B}(-1,6,3)$ and perpendicular to the line $\frac{x-3}{-2}=\frac{y}{3}=\frac{z-1}{1}$, is
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If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta, \gamma)$, then $\alpha + \beta + \gamma$ is equal to:
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Consider the line $L$ passing through the points $(1,2,3)$ and $(2,3,5)$.
The distance of the point $\left(\dfrac{11}{3},\dfrac{11}{3},\dfrac{19}{3}\right)$ from the line $L$ along the line
$\dfrac{3x-11}{2}=\dfrac{3y-11}{1}=\dfrac{3z-19}{2}$ is equal to:
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If the two lines $x+(a-1)y=1$ and $2x+a^{2}y=1$ $(a\in\mathbb{R}\setminus{0,1})$ are perpendicular, then the distance of their point of intersection from the origin is:
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The shortest distance between the lines
\[
\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}
\quad\text{and}\quad
\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}
\]
is:
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Solution
Let a variable line passing through the centre of the circle
$x^{2}+y^{2}-16x-4y=0$ meet the positive coordinate axes at the points $A$ and $B$.
Then the minimum value of $OA+OB$, where $O$ is the origin, is:
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If the length of the perpendicular from the point $(\beta,0,\beta)\ (\beta\ne0)$ to the line, $\dfrac{x}{1}=\dfrac{y-1}{0}=\dfrac{z+1}{-1}$ is $\sqrt{\dfrac{3}{2}}$, then $\beta$ is equal to:
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Solution
The lines x = ay $-$ 1 = z $-$ 2 and x = 3y $-$ 2 = bz $-$ 2, (ab $\ne$ 0) are coplanar, if :
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Solution
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