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Straight Lines and Pair of Straight Lines
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Previous Years Questions
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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
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The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose su...
WB JEE 2020
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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
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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
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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
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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
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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
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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
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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
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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$$\...
WB JEE 2021
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A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutt...
WB JEE 2020
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A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. Th...
WB JEE 2020
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Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the ori...
WB JEE 2020
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The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents
WB JEE 2020
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If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by $$-$$ d = 0 lies in the 4th quadrant and is eq...
WB JEE 2019
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A variable line passes through the fixed point $$(\alpha ,\beta )$$. The locus of the foot of the perpendicular from the...
WB JEE 2019
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A straight line through the point (3, $$-$$2) is inclined at an angle 60$$^\circ$$ to the line $$\sqrt 3 x + y = 1$$. If...
WB JEE 2019
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A variable line passes through a fixed point $$({x_1},{y_1})$$ and meets the axes at A and B. If the rectangle OAPB be c...
WB JEE 2019
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A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, $$-$$3). A variable line PQ is drawn perpendicular to AB cuttin...
WB JEE 2018
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The angular points of a triangle are A($$-$$ 1, $$-$$ 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle...
WB JEE 2018
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The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y = ...
WB JEE 2018
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Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line $$7x - 9y + 10 = 0$$ upon the lines ...
WB JEE 2017
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The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = $$-...
WB JEE 2017
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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
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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
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The equation of the locus of the point of intersection of the straight lines $$x\sin \theta + (1 - \cos \theta )y = a\s...
WB JEE 2011
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If the three points A(1, 6), B(3, $$-$$4) and C(x, y) are collinear then the equation satisfying by x and y is
WB JEE 2011
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The coordinates of the two points lying on x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are...
WB JEE 2011
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The equations of the lines through (1, 1) and making angles of 45$$^\circ$$ with the line x + y = 0 are
WB JEE 2010
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The equations $$y = \pm \sqrt {3x} $$, y = 1 are the sides of
WB JEE 2010
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If the three points (3q, 0) (0, 3p) and (1, 1) are collinear then which one is true?
WB JEE 2010
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If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is a/...
WB JEE 2010
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The straight line 3x + y = 9 divides the line segment joining the points (1, 3) and (2, 7) in the ratio
WB JEE 2010
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The point ($$-$$4, 5) is the vertex of a square and one of its diagonals is 7x $$-$$ y + 8 = 0. The equation of the othe...
WB JEE 2009
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The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is
WB JEE 2009
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If C is the reflection of A(2, 4) in x-axis and B is the reflection of C in y-axis, then $$|AB|$$ is
WB JEE 2009
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A line through the point A(2, 0) which makes an angle of 30$$^\circ$$ with the positive direction of x-axis is rotated a...
WB JEE 2009
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The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are
WB JEE 2009
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If C is a point on the line segment joining A($$-$$3, 4) and B(2, 1) such that AC = 2BC, then the coordinate of C is...
WB JEE 2009
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The co-ordinates of the foot of perpendicular from (a, 0) on the line $$y = mx + {a \over m}$$ are
WB JEE 2008
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The distance between the lines $$5x - 12y + 65 = 0$$ and $$5x - 12y - 39 = 0$$ is
WB JEE 2008
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One possible condition for the three points (a, b), (b, a) and (a2, $$-$$ b2) to be collinear is...
WB JEE 2008
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Find the image of the point ($$-$$8, 12) with respect to the line 4x + 7y + 13 = 0.
WB JEE 2011
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The equations to the pairs of opposite sides of a parallelogram are x2 $$-$$ 5x + 6 = 0 and y2 $$-$$ 6y + 5 = 0. Find th...
WB JEE 2009
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If 2a $$-$$ 5b $$-$$ 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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