PrepWiser › Learn › Mathematics › Straight LinesStraight Lines — JEE Main PYQs & Practice Questions Straight Lines is a Mathematics chapter in the JEE Main syllabus. This page brings together 123 previous-year and practice questions on Straight Lines, organised into 6 topics: Distance and Section Formula, Forms of a Line, Angle Between Lines, Distance from a Point to a Line, Family of Lines and Locus. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Distance and Section Formula Let A be the set of all points (α, β) such that the area of triangle formed by the… Let the area of the triangle with vertices A(1, α), B(α, 0) and C(0, α) be 4 sq. units… If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = mx… The equations of the sides AB, BC and CA of a triangle ABC are : 2x+y=0,x+py=21a,(a± 0)… Let A(1, 0), B(6, 2) and C (3/2,6) be the vertices of a triangle ABC. If P is a Point… A man starts walking from the point P(-3, 4), touches the x-axis at R, and then turns to… Let A(a, 0), B(b, 2b + 1) and C(0, b), b ≠ 0, |b| ≠ 1, be points such that the area of… Let A(-1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0… Let C(α,β) be the circumcenter of the triangle formed by the lines 4x+3y=69 4y-3x=17… A rod of length eight units moves such that its ends A and B always lie on the lines… Let α₁, α₂ (α₁ < α₂) be the values of α fo the points (α, -3), (2, 0) and (1, α) to be… Let the area of the triangle formed by a straight line L:x+by+c=0 with co-ordinate axes… In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is… The distance between the two points A and A' which lie on y = 2 such that both the line… The equations of two sides AB and AC of a triangle ABC are 4x+y=14 and 3x-2y=5… Let the points of intersections of the lines x - y + 1 = 0, x - 2y + 3 = 0 and 2x - 5y +… The equations of the sides AB,BC and CA of a triangle ABC are 2x+y=0,x+py=39 and x-y=3… Let the three sides of a triangle are on the lines 4x-7y+10=0,x+y=5 and 7x+4y=15. Then… The equations of the sides AB,BC and CA of a triangle ABC are 2x+y=0,x+py=15a and x-y=3… In an equilateral triangle PQR, let the vertex P be at (3,5) and the side QR be along… Forms of a Line A line passing through the point A(9,0) makes an angle of 30° with the positive… The straight lines l₁ and l₂ pass through the origin and trisect the line segment of the… A man is walking on a straight line. The arithmetic mean of the reciprocals of the… A ray of light coming from the point P(1,2) gets reflected from the point Q on the… Let a variable line passing through the centre of the circle x²+y²-16 x-4 y=0, meet the… Let the points (11/2,α) lie on or inside the triangle with sides x+y=11,x+2y=16 and… Let m₁,m₂ be the slopes of two adjacent sides of a square of side a such that… A line, with the slope greater than one, passes through the point A(4,3) and intersects… If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3)… Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively… Let A(-2,-1),B(1,0),C(α,β) and D(γ,δ) be the vertices of a parallelogram ABCD. If the… A line passing through the point P(a, 0) makes an acute angle α with the positive… The set of all possible values of θ in the interval (0, π) for which the points (1, 2)… The number of integral values of m so that the abscissa of point of intersection of… Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the… Let a variable line of slope m>0 passing through the point (4,-9) intersect the… From the point (-1,-1), two rays are sent making angles of 45° with the line x+y=0… A ray of light coming from the point (2, 2√3) is incident at an angle 30ᵒ on the line x… A light ray emits from the origin making an angle 30° with the positive x-axis. After… Let R be the interior region between the lines 3x-y+1=0 and x+2y-5=0 containing the… Angle Between Lines Let the line L₁:x+3=0 intersect the lines L₂:x-y=0 and L₃:3x+y=0 at the points A and B… The equation of one of the straight lines which passes through the point (1, 3) and… Let a ray of light passing through the point (3,10) reflects on the line 2x+y=6 and the… Let A,B be points on the two half-lines x-√3|y|=α,α>0 at a distance of α from their… If the line segment joining the points (5,2) and (2,a) subtends an angle π/4 at the… Let A(1,0),B(2,-1) and C(7/3,4/3) be three points. If the equation of the bisector of… Let the angles made with the positive x-axis by two straight lines drawn from the point… Let ABC be an isosceles triangle in which A is at (-1,0),∠ A=2π/3,AB=AC and B is on the… The portion of the line 4x+5y=20 in the first quadrant is trisected by the lines L₁ and… Two equal sides of an isosceles triangle are along -x+2y=4 and x+y=4. If m is the slope… Let two straight lines drawn from the origin O intersect the line 3x+4y=12 at the points… In a △ ABC, suppose y=x is the equation of the bisector of the angle B and the equation… Distance from a Point to a Line Let a point A lie between the parallel lines L₁ and L₂ such that its distances from L₁… If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec α… Let PQ be a diameter of the circle x² + y² = 9. If α and β are the lengths of the… If the sum of squares of all real values of α, for which the lines 2x-y+3=0,6x+3y+1=0… Let the point P(α,β) be at a unit distance from each of the two lines L₁:3x-4y+12=0, and… Let the equation x(x+2)(12-k)=2 have equal roots. Then the distance of the point (k… If α=1+Σᵣ₌₁⁶(-3)ʳ⁻¹ ¹² C₂ᵣ₋₁, then the distance of the point (12, √3) from the line α… Let a be the length of a side of a square OABC with O being the origin. Its side OA… If x²-y²+2hxy+2gx+2fy+c=0 is the locus of a point, which moves such that it is always… Consider the lines x(3λ+1)+y(7λ+2)=17λ+5,λ being a parameter, all passing through a… A line passes through the origin and makes equal angles with the positive coordinate… Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the… If the image of the point (-4,5) in the line x+2 y=2 lies on the circle… Let A be the point of intersection of the lines 3x+2y=14,5x-y=6 and B be the point of… Let A(a,b),B(3,4) and C(-6,-8) respectively denote the centroid, circumcentre and… The distance of the point (2,3) from the line 2x-3y+28=0, measured parallel to the line… A rectangle is formed by the lines x=0,y=0,x=3 and y=4. Let the line L be perpendicular… Let the equations of two adjacent sides of a parallelogram ABCD be 2x-3y=-23 and… If the line, 2x - y + 3 = 0 is at a distance 1/√5 and 2/√5 from the lines 4x - 2y + α =… The vertices of a triangle are A(-1,3),B(-2,2) and C(3,-1). A new triangle is formed by… Family of Lines Locus The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y… Let a point P be such that its distance from the point (5, 0) is thrice the distance of… Let R be a rectangle given by the lines x=0, x=2, y=0 and y=5. Let A(α,0) and… If the point (α,7√3/3) lies on the curve traced by the mid-points of the line segments… A point P moves so that the sum of squares of its distances from the points (1,2) and… A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is : A square ABCD has all its vertices on the curve x²y² = 1. The midpoints of its sides… If the locus of the point, whose distances from the point (2,1) and (1,3) are in the… Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of… If A and B are the points of intersection of the circle x²+y²-8x=0 and the hyperbola… Let A(-1,1) and B(2,3) be two points and P be a variable point above the line AB such… Let A be the point (1,2) and B be any point on the curve x²+y²=16. If the centre of the… The locus of a point, which moves such that the sum of squares of its distances from the… More Mathematics chapters Frequently asked questions How many Straight Lines questions are there for JEE Main? PrepWiser has 123 Straight Lines questions for JEE Main, grouped into 6 topics such as Distance and Section Formula, Forms of a Line and Angle Between Lines.
Are these Straight Lines questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Straight Lines questions? Open any Straight Lines question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.