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Straight Lines and Pair of Straight Lines

576 Questions Start JEE Mains Test
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET BITSAT
1988 Q551 JEE Advanced MCQ
14 Mar 2026
The lines $2x + 3y + 19 = 0$ and $9x + 6y - 17 = 0$ cut the coordinates axes in concyclic points.
A.
TRUE
B.
FALSE
1986 Q552 JEE Advanced MCQ
14 Mar 2026
The points $\left( {0,{8 \over 3}} \right),\,\,\left( {1,\,3} \right)$ and $\left( {82,\,30} \right)$ are vertices of
A.
an obtuse angled triangle
B.
an acute angled triangle
C.
a right angled triangle
D.
none of these
1986 Q553 JEE Advanced MCQ
14 Mar 2026
A vector $\overline a $ has components $2p$ and $1$ with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, $\overline a $ has components $p + 1$ and $1$, then
A.
$p = 0$
B.
$p = 1$ or $p = - {1 \over 3}$
C.
$\,p = - 1$ or $p = {1 \over 3}$
D.
$p = 1$ or $p = -1$
1986 Q554 JEE Advanced MSQ
14 Mar 2026
All points lying inside the triangle formed by the points $\left( {1,\,3} \right),\,\left( {5,\,0} \right)$ and $\left( { - 1,\,2} \right)$ satisfy
A.
$3x + 2y \ge 0$
B.
$2x + y - 13 \ge 0$
C.
$2x - 3y - 12 \le 0$
D.
$ - 2x + y \ge 0$
1985 Q555 JEE Advanced MSQ
14 Mar 2026
Three lines $px + qy + r = 0$, $qx + ry + p = 0$ and $rx + py + q = 0$ are concurrent if
A.
$p + q + r = 0$
B.
${p^2} + {q^2} + {r^2} = qr + rp + pq$
C.
${p^3} + {q^3} + {r^3} = 3pqr$
D.
none of these.
1985 Q556 JEE Advanced Numerical
14 Mar 2026
One of the diameters of the circle circumscribing the rectangle $ABCD$ is $4y = x + 7$. If $A$ and $B$ are the points $(-3, 4)$ and $(5, 4)$ respectively, then find the area of rectangle.
1985 Q557 JEE Advanced Numerical
14 Mar 2026
Two sides of rhombus $ABCD$ are parallel to the lines $y = x + 2$ and $y = 7x + 3$. If the diagonals of the rhombus intersect at the point $(1, 2)$ and the vertex $A$ is on the $y$-axis, find possible co-ordinates of $A$.
1985 Q558 JEE Advanced Numerical
14 Mar 2026
The orthocentre of the triangle formed by the lines $x + y = 1,\,2x + 3y = 6$ and $4x - y + 4 = 0$ lies in quadrant number .............
1984 Q559 JEE Advanced Numerical
14 Mar 2026
Two equal sides of an isosceles triangle are given by the equations $7x - y + 3 = 0$ and $x + y - 3 = 0$ and its thirds side passes through the point $(1, -10)$. Determine the equation of the third side.
1984 Q560 JEE Advanced Numerical
14 Mar 2026
If $a,\,b$ and $c$ are in A.P., then the straight line $ax + by + c = 0$ will always pass through a fixed point whose coordinates are ...............
1983 Q561 JEE Advanced MCQ
14 Mar 2026
The straight lines $x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$ form a triangle which is
A.
isosceles
B.
equilateral
C.
right angled
D.
none of these
1983 Q562 JEE Advanced Numerical
14 Mar 2026
The vertices of a triangle are
$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3},a\left( {{t_2} + {t_3}} \right)} \right],\,\,\left[ {a{t_3}{t_1},\,a\left( {{t_3} + {t_1}} \right)} \right]$. Find the orthocentre of the triangle.
1983 Q563 JEE Advanced Numerical
14 Mar 2026
The end $A, B$ of a straight line segment of constant length $c$ slide upon the fixed rectangular axes $OX, OY$ respectively. If the rectangle $OAPB$ be completed, then show that the locus of the foot of the perpendicular drawn from $P$ to $AB$ is ${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {c^{{2 \over 3}}}$
1983 Q564 JEE Advanced Numerical
14 Mar 2026
The coordinates of $A, B, C$ are $(6, 3), (-3, 5), (4, -2)$ respectively, and $P$ is any point $(x, y)$. Show that the ratio of the area of the triangles $\Delta $ $PBC$ and $\Delta $$ABC$ is $\left| {{{x + y - 2} \over 7}} \right|$
1983 Q565 JEE Advanced Numerical
14 Mar 2026
Given the points $A\left( {0,4} \right)$ and $B\left( {0, - 4} \right)$, the equation of the locus of the point $P\left( {x,y} \right)$ such that $\left| {AP - BP} \right| = 6$ is .............
1983 Q566 JEE Advanced MCQ
14 Mar 2026
The straight line $5x + 4y = 0$ passes through the point of intersection of the straight lines $x + 2y - 10 = 0$ and $2x + y + 5 = 0.$
A.
TRUE
B.
FALSE
1982 Q567 JEE Advanced Numerical
14 Mar 2026
$y = {10^x}$ is the reflection of ${\log _{10}}\,x$ in the line whose equation is ...........
1982 Q568 JEE Advanced Numerical
14 Mar 2026
The set of lines $ax + by + c = 0,$ where $3a + 2b + 4c = 0$ is concurrent at the point ..........
1981 Q569 JEE Advanced Numerical
14 Mar 2026
The area enclosed within the curve $\left| x \right| + \left| y \right| = 1$ is .................
1980 Q570 JEE Advanced MCQ
14 Mar 2026
The point $\,\left( {4,\,1} \right)$ undergoes the following three transformations successively.
Reflection about the line $y=x$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $p/4$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.
A.
$\left( {{1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$
B.
$\left( { - \sqrt 2 ,\,7\sqrt 2 } \right)$
C.
$\left( { - {1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$
D.
$\left( { \sqrt 2 ,\,7\sqrt 2 } \right)$
1980 Q571 JEE Advanced Numerical
14 Mar 2026
A straight line $L$ is perpendicular to the line $5x - y = 1.$ The area of the triangle formed by the line $L$ and the coordinate axes is $5$. Find the equation of the Line $L$.
1979 Q572 JEE Advanced MCQ
14 Mar 2026
The points $\left( { - a,\, - b} \right),\,\left( {0,\,0} \right),\,\left( {a,\,b} \right)$ and $\left( {{a^2},\,ab} \right)$ are :
A.
Collinear
B.
Vertices of a parallelogram
C.
Vertices of a rectangle
D.
None of these
1979 Q573 JEE Advanced Numerical
14 Mar 2026
(a) Two vertices of a triangle are $(5, -1)$ and $(-2, 3).$ If the orthocentre of the triangle is the origin, find the coordinates of the third point.
(b) Find the equation of the line which bisects the obtuse angle between the lines $x - 2y + 4 = 0$ and $4x - 3y + 2 = 0$.
1978 Q574 JEE Advanced Numerical
14 Mar 2026
A straight line segment of length $\ell $ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $1 : 2$
1978 Q575 JEE Advanced Numerical
14 Mar 2026
One side of rectangle lies along the line $4x + 7y + 5 = 0.$ Two of its vertices are $(-3, 1)$ and $(1, 1).$ Find the equations of the other three sides.
1978 Q576 JEE Advanced Numerical
14 Mar 2026
The area of a triangle is $5$. Two of its vertices are $A\left( {2,1} \right)$ and $B\left( {3, - 2} \right)$. The third vertex $C$ lies on $y = x + 3$. Find $C$.