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JEE Advanced

Straight Lines and Pair of Straight Lines

Mathematics

Previous Years Questions

Numerical

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Consider the lines L1 and L2 defined by $${L_1}:x\sqrt 2 + y - 1 = 0$$ and $${L_2}:x\sqrt 2 - y + 1 = 0$$For a fixed c...
JEE Advanced 2021 Paper 1 Online
Consider the lines L1 and L2 defined by $${L_1}:x\sqrt 2 + y - 1 = 0$$ and $${L_2}:x\sqrt 2 - y + 1 = 0$$For a fixed c...
JEE Advanced 2021 Paper 1 Online
For a point $$P$$ in the plane, Let $${d_1}\left( P \right)$$ and $${d_2}\left( P \right)$$ be the distance of the point...
JEE Advanced 2014 Paper 1 Offline

MCQ (Single Correct Answer)

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For $$a > b > c > 0,$$ the distance between $$(1, 1)$$ and the point of intersection of the lines $$ax + by + c...
JEE Advanced 2013 Paper 1 Offline
A straight line $$L$$ through the point $$(3, -2)$$ is inclined at an angle $${60^ \circ }$$ to the line $$\sqrt {3x} +...
IIT-JEE 2011 Paper 1 Offline
The lines $${L_1}:y - x = 0$$ and $${L_2}:2x + y = 0$$ intersect the line $${L_3}:y + 2 = 0$$ at $$P$$ and $$Q$$ respect...
IIT-JEE 2007
Let $$O\left( {0,0} \right),P\left( {3,4} \right),Q\left( {6,0} \right)$$ be the vertices of the triangles $$OPQ$$. The ...
IIT-JEE 2007
Area of the triangle formed by the line $$x + y = 3$$ and angle bisectors of the pair of straight line $${x^2} - {y^2} ...
IIT-JEE 2004 Screening
Orthocentre of triangle with vertices $$\left( {0,0} \right),\left( {3,4} \right)$$ and $$\left( {4,0} \right)$$ is
IIT-JEE 2003 Screening
The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of t...
IIT-JEE 2003 Screening
The pair of lines represented by $$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$ are perpendicular to each othe...
IIT-JEE 2002
If the pair of lines $$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$ intersect on the $$y$$ axis then
IIT-JEE 2002
Locus of mid point of the portion between the axes of $$x$$ $$\cos \alpha + y\sin \alpha = p$$ where $$p$$ is constant...
IIT-JEE 2002
A triangle with vertices $$(4, 0), (-1, -1), (3, 5)$$is
IIT-JEE 2002
A straight line through the origin $$O$$ meets the parallel lines $$4x+2y=9$$ and $$2x+y+6=0$$ at points $$P$$ and $$Q$$...
IIT-JEE 2002 Screening
Let $$P = \left( { - 1,\,0} \right),\,Q = \left( {0,\,0} \right)$$ and $$R = \left( {3,\,3\sqrt 3 } \right)$$ be three p...
IIT-JEE 2002 Screening
Let $$0 < \alpha < {\pi \over 2}$$ be fixed angle. If $$P = \left( {\cos \theta ,\,\sin \theta } \right)$$ and $...
IIT-JEE 2002 Screening
Area of the parallelogram formed by the lines $$y = mx$$, $$y = mx + 1$$, $$y = nx$$ and $$y = nx + 1$$ equals
IIT-JEE 2001 Screening
The number of integer values of $$m$$, for which the $$x$$-coordinate of the point of intersection of the lines $$3x + 4...
IIT-JEE 2001 Screening
The incentre of the triangle with vertices $$\left( {1,\,\sqrt 3 } \right),\left( {0,\,0} \right)$$ and $$\left( {2,\,0}...
IIT-JEE 2000 Screening
Let $$PS$$ be the median of the triangle with vertices $$P(2, 2),$$ $$Q(6, -1)$$ and $$R(7, 3).$$ The equation of the li...
IIT-JEE 2000 Screening
If $${x_1},\,{x_2},\,{x_3}$$ as well as $${y_1},\,{y_2},\,{y_3}$$, are in G.P. with the same common ratio, then the poin...
IIT-JEE 1999
Lt $$PQR$$ be a right angled isosceles triangle, right angled at $$P(2, 1)$$. If the equation of the line $$QR$$ is $$2x...
IIT-JEE 1999
If $$\left( {P\left( {1,2} \right),\,Q\left( {4,6} \right),\,R\left( {5,7} \right)} \right)$$ and $$S\left( {a,b} \right...
IIT-JEE 1998
The diagonals of a parralleogram $$PQRS$$ are along the lines $$x + 3y = 4$$ and $$6x - 2y = 7$$. Then $$PQRS$$ must be ...
IIT-JEE 1998
The orthocentre of the triangle formed by the lines $$xy=0$$ and $$x+y=1$$ is
IIT-JEE 1995
The equations to a pair of opposites sides of parallelogram are $${x^2} - 5x + 6 = 0$$ and $${y^2} - 6y + 5 = 0,$$ the e...
IIT-JEE 1994
The locus of a variable point whose distance from $$\left( { - 2,\,0} \right)$$ is $$2/3$$ times its distance from the ...
IIT-JEE 1994
If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
IIT-JEE 1992
Line $$L$$ has intercepts $$a$$ and $$b$$ on the coordinate axes. When the axes are rotated through a given angle, keepi...
IIT-JEE 1990
If $$P=(1, 0),$$ $$Q=(-1, 0)$$ and $$R=(2, 0)$$ are three given points, then locus of the point $$S$$ satisfying the rel...
IIT-JEE 1988
A vector $$\overline a $$ has components $$2p$$ and $$1$$ with respect to a rectangular cartesian system. This system is...
IIT-JEE 1986
The points $$\left( {0,{8 \over 3}} \right),\,\,\left( {1,\,3} \right)$$ and $$\left( {82,\,30} \right)$$ are vertices o...
IIT-JEE 1986
The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triangle which is
IIT-JEE 1983
The point $$\,\left( {4,\,1} \right)$$ undergoes the following three transformations successively. Reflection about the ...
IIT-JEE 1980
The points $$\left( { - a,\, - b} \right),\,\left( {0,\,0} \right),\,\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} ...
IIT-JEE 1979

Subjective

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The area of the triangle formed by intersection of a line parallel to $$x$$-axis and passing through $$P (h, k)$$ with t...
IIT-JEE 2005
A straight line $$L$$ with negative slope passes through the point $$(8, 2)$$ and cuts the positive coordinate axes at p...
IIT-JEE 2002
A straight line $$L$$ through the origin meets the lines $$x + y = 1$$ and $$x + y = 3$$ at $$P $$ and $$Q$$ respectivel...
IIT-JEE 2002
Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that the equation $$\left| {\matrix{ {ax -...
IIT-JEE 2001
Let $$ABC$$ and $$PQR$$ be any two triangles in the same plane. Assume that the prependiculars from the points $$A, B, C...
IIT-JEE 2000
For points $$P\,\,\, = \left( {{x_1},\,{y_1}} \right)$$ and $$Q\,\,\, = \left( {{x_2},\,{y_2}} \right)$$ of the co-ordin...
IIT-JEE 2000
Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.
IIT-JEE 1998
A rectangle $$PQRS$$ has its side $$PQ$$ parallel to the line $$y = mx$$ and vertices $$P, Q$$ and $$S$$ on the lines $$...
IIT-JEE 1996
A line through $$A (-5, -4)$$ meets the line $$x + 3y + 2 = 0,$$ $$2x + y + 4 = 0$$ and $$x - y - 5 = 0$$ at the points...
IIT-JEE 1993
Tagent at a point $${P_1}$$ {other than $$(0, 0)$$} on the curve $$y = {x^3}$$ meets the curve again at $${P_2}$$. The t...
IIT-JEE 1993
Determine all values of $$\alpha $$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the tria...
IIT-JEE 1992
Find the equation of the line passing through the point $$(2, 3)$$ and making intercept of length 2 units between the li...
IIT-JEE 1991
Show that all chords of the curve $$3{x^2} - {y^2} - 2x + 4y = 0,$$ which subtend a right angle at the origin, pass thro...
IIT-JEE 1991
Straight lines $$3x + 4y = 5$$ and $$4x - 3y = 15$$ intersect at the point $$A$$. Points $$B$$ and $$C$$ are choosen on ...
IIT-JEE 1990
A line cuts the $$x$$-axis at $$A (7, 0)$$ and the $$y$$-axis at $$B (0, -5)$$. A variable line $$PQ$$ is drawn perpendi...
IIT-JEE 1990
Let $$ABC$$ be a triangle with $$AB = AC$$. If $$D$$ is the midpoint of $$BC, E$$ is the foot of the perpendicular drawn...
IIT-JEE 1989
Lines$${L_1} = ax + by + c = 0$$ and $${L_2} = lx + my + n = 0$$ intersect at the point $$P$$ and make an angle $$\theta...
IIT-JEE 1988
Two sides of rhombus $$ABCD$$ are parallel to the lines $$y = x + 2$$ and $$y = 7x + 3$$. If the diagonals of the rhombu...
IIT-JEE 1985
One of the diameters of the circle circumscribing the rectangle $$ABCD$$ is $$4y = x + 7$$. If $$A$$ and $$B$$ are the p...
IIT-JEE 1985
Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3 = 0$$ and $$x + y - 3 = 0$$ and its thi...
IIT-JEE 1984
The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon the fixed rectangular axes $$OX, OY$$ re...
IIT-JEE 1983
The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show ...
IIT-JEE 1983
The vertices of a triangle are $$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3...
IIT-JEE 1983
A straight line $$L$$ is perpendicular to the line $$5x - y = 1.$$ The area of the triangle formed by the line $$L$$ and...
IIT-JEE 1980
(a) Two vertices of a triangle are $$(5, -1)$$ and $$(-2, 3).$$ If the orthocentre of the triangle is the origin, find t...
IIT-JEE 1979
One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find ...
IIT-JEE 1978
A straight line segment of length $$\ell $$ moves with its ends on two mutually perpendicular lines. Find the locus of t...
IIT-JEE 1978
The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)$$ and $$B\left( {3, - 2} \right)$$. The...
IIT-JEE 1978

MCQ (More than One Correct Answer)

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Let $${L_1}$$ be a straight line passing through the origin and $${L_2}$$ be the straight line $$x + y = 1$$. If the int...
IIT-JEE 1999
If the vertices $$P, Q, R$$ of a triangle $$PQR$$ are rational points, which of the following points of the triangle $$P...
IIT-JEE 1998
All points lying inside the triangle formed by the points $$\left( {1,\,3} \right),\,\left( {5,\,0} \right)$$ and $$\lef...
IIT-JEE 1986
Three lines $$px + qy + r = 0$$, $$qx + ry + p = 0$$ and $$rx + py + q = 0$$ are concurrent if
IIT-JEE 1985

Fill in the Blanks

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The vertices of a triangle are $$A\left( { - 1, - 7} \right)B\left( {5,\,1} \right)$$ and $$C\left( {1,\,4} \right).$$ T...
IIT-JEE 1993
Let the algebraic sum of the perpendicular distances from the points $$\left( {2,0} \right),\,\left( {0,\,2} \right)$$ $...
IIT-JEE 1991
The orthocentre of the triangle formed by the lines $$x + y = 1,\,2x + 3y = 6$$ and $$4x - y + 4 = 0$$ lies in quadrant ...
IIT-JEE 1985
If $$a,\,b$$ and $$c$$ are in A.P., then the straight line $$ax + by + c = 0$$ will always pass through a fixed point wh...
IIT-JEE 1984
Given the points $$A\left( {0,4} \right)$$ and $$B\left( {0, - 4} \right)$$, the equation of the locus of the point $$P\...
IIT-JEE 1983
The set of lines $$ax + by + c = 0,$$ where $$3a + 2b + 4c = 0$$ is concurrent at the point ..........
IIT-JEE 1982
$$y = {10^x}$$ is the reflection of $${\log _{10}}\,x$$ in the line whose equation is ...........
IIT-JEE 1982
The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ is .................
IIT-JEE 1981

True or False

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The lines $$2x + 3y + 19 = 0$$ and $$9x + 6y - 17 = 0$$ cut the coordinates axes in concyclic points.
IIT-JEE 1988
The straight line $$5x + 4y = 0$$ passes through the point of intersection of the straight lines $$x + 2y - 10 = 0$$ and...
IIT-JEE 1983

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