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WB JEE

Straight Lines and Pair of Straight Lines

Mathematics

Previous Years Questions

MCQ (More than One Correct Answer)

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Consider the equation $$y - {y_1} = m(x - {x_1})$$. If m and x1 are fixed and different lines are drawn for different va...
WB JEE 2022
The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose su...
WB JEE 2020
Straight lines x $$-$$ y = 7 and x + 4y = 2 intersect at B. Points A and C are so chosen on these two lines such that AB...
WB JEE 2019
The area of the triangle formed by the intersection of a line parallel to X-axis and passing through P(h, k), with the l...
WB JEE 2018

MCQ (Single Correct Answer)

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If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is
WB JEE 2022
If the algebraic sum of the distances from the points (2, 0), (0, 2) and (1, 1) to a variable straight line be zero, the...
WB JEE 2022
A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching X-axis, the equation of the reflected ray...
WB JEE 2021
A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, B respectively such that the area of the...
WB JEE 2021
Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular...
WB JEE 2021
If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos$$\theta$$, b sin$$\...
WB JEE 2021
A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutt...
WB JEE 2020
A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. Th...
WB JEE 2020
Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the ori...
WB JEE 2020
The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents
WB JEE 2020
If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by $$-$$ d = 0 lies in the 4th quadrant and is eq...
WB JEE 2019
A variable line passes through the fixed point $$(\alpha ,\beta )$$. The locus of the foot of the perpendicular from the...
WB JEE 2019
A straight line through the point (3, $$-$$2) is inclined at an angle 60$$^\circ$$ to the line $$\sqrt 3 x + y = 1$$. If...
WB JEE 2019
A variable line passes through a fixed point $$({x_1},{y_1})$$ and meets the axes at A and B. If the rectangle OAPB be c...
WB JEE 2019
A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, $$-$$3). A variable line PQ is drawn perpendicular to AB cuttin...
WB JEE 2018
The angular points of a triangle are A($$-$$ 1, $$-$$ 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle...
WB JEE 2018
The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y = ...
WB JEE 2018
Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line $$7x - 9y + 10 = 0$$ upon the lines ...
WB JEE 2017
The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = $$-...
WB JEE 2017
Let A(2, $$-$$3) and B($$-$$ 2, 1) be two angular points of $$\Delta$$ABC. If the centroid of the triangle moves on the ...
WB JEE 2017
Transforming to parallel axes through a point (p, q), the equation $$2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0$$ becomes ...
WB JEE 2017
The equation of the locus of the point of intersection of the straight lines $$x\sin \theta + (1 - \cos \theta )y = a\s...
WB JEE 2011
If the three points A(1, 6), B(3, $$-$$4) and C(x, y) are collinear then the equation satisfying by x and y is
WB JEE 2011
The coordinates of the two points lying on x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are...
WB JEE 2011
The equations of the lines through (1, 1) and making angles of 45$$^\circ$$ with the line x + y = 0 are
WB JEE 2010
The equations $$y = \pm \sqrt {3x} $$, y = 1 are the sides of
WB JEE 2010
If the three points (3q, 0) (0, 3p) and (1, 1) are collinear then which one is true?
WB JEE 2010
If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is a/...
WB JEE 2010
The straight line 3x + y = 9 divides the line segment joining the points (1, 3) and (2, 7) in the ratio
WB JEE 2010
The point ($$-$$4, 5) is the vertex of a square and one of its diagonals is 7x $$-$$ y + 8 = 0. The equation of the othe...
WB JEE 2009
The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is
WB JEE 2009
If C is the reflection of A(2, 4) in x-axis and B is the reflection of C in y-axis, then $$|AB|$$ is
WB JEE 2009
A line through the point A(2, 0) which makes an angle of 30$$^\circ$$ with the positive direction of x-axis is rotated a...
WB JEE 2009
The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are
WB JEE 2009
If C is a point on the line segment joining A($$-$$3, 4) and B(2, 1) such that AC = 2BC, then the coordinate of C is...
WB JEE 2009
The co-ordinates of the foot of perpendicular from (a, 0) on the line $$y = mx + {a \over m}$$ are
WB JEE 2008
The distance between the lines $$5x - 12y + 65 = 0$$ and $$5x - 12y - 39 = 0$$ is
WB JEE 2008
One possible condition for the three points (a, b), (b, a) and (a2, $$-$$ b2) to be collinear is...
WB JEE 2008

Subjective

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Find the image of the point ($$-$$8, 12) with respect to the line 4x + 7y + 13 = 0.
WB JEE 2011
The equations to the pairs of opposite sides of a parallelogram are x2 $$-$$ 5x + 6 = 0 and y2 $$-$$ 6y + 5 = 0. Find th...
WB JEE 2009
If 2a $$-$$ 5b $$-$$ 3c = 0, show that the straight line ax + by + c = 0 always passes through a fixed point. Find the e...
WB JEE 2008

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