Straight Line Equations: JEE Questions & Solutions

A rectangle is formed by the lines x = 0, y = 0, x = 3 and y = 4. Let the line L be perpendicular to 3x + y + 6 = 0 and divide the area of…

Let A(1, 2) and C(-3, -6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line 7x - y = 14. If…

Let A(1,0), B(2,-1) and C(7/3,4/3) be three points. If the equation of the bisector of the angle ABC is α x+β y=5, then the value of α²+β²…

Let the angles made with the positive x-axis by two straight lines drawn from the point P(2,3) and meeting the line x+y=6 at a distance…

Let the distance between two parallel lines be 5 units and a point P lies between the lines at a unit distance from one of them. An…

Let the lines 3x - 4y - α = 0, 8x - 11y - 33 = 0, 2x - 3y + λ = 0 be concurrent. If the image of the point (1, 2) in the line 2x - 3y + λ =…

Let the points ( 11/2, α) lie on or inside the triangle with sides x + y = 11, x + 2y = 16, and 2x + 3y = 29. Then the product of the…

If a = 1 + Σ_(r=1)⁶ (-3)^(r-1) C(12,2r-1), then the distance of the point (12, √3) from the line α x - √3y + 1 = 0 is:

Two equal sides of an isosceles triangle are along -x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum of all…

Let ABC be a triangle formed by the lines 7x - 6y + 3 = 0, x + 2y - 31 = 0, and 9x - 2y - 19 = 0. Let the point (h, k) be the image of the…

Let the area of the triangle formed by a straight line L: x + by + c = 0 with co-ordinate axes be 48 square units. If the perpendicular…

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines L₁: 2x + y + 6 = 0 and…

Consider the lines x(3λ + 1) + y(7λ + 2) = 17λ + 5, λ being a parameter, all passing through a point P. One of these lines (say L) is…

Let the equation x(x+2)(12-k) = 2 have equal roots. The distance of the point (k, k/2) from the line 3x + 4y + 5 = 0 is

Let ABC be the triangle such that the equations of lines AB and AC are: 3y - x = 2 and x + y = 2, respectively, and the points B and C lie…

A line passing through the point P(a, 0) makes an acute angle α with the positive x-axis. Let this line be rotated about the point P…

The portion of the line 4x + 5y = 20 in the first quadrant is trisected by lines L₁ and L₂ passing through the origin. The tangent of the…

Let R be the region between lines 3x - y + 1 = 0 and x + 2y - 5 = 0 containing the origin. Find values of a for which (a², a + 1) lie in R:

If the sum of squares of all real values of α, for which the lines 2x - y + 3 = 0, 6x + 3y + 1 = 0, and α x + 2y - 2 = 0 do not form a…

In a △ ABC, suppose y = x is the equation of the bisector of angle B, and the equation of side AC is 2x - y = 2. If 2AB = BC and the points…

The distance of the point (2, 3) from the line 2x - 3y + 28 = 0, measured parallel to the line √3x - y + 1 = 0, is equal to:

Let A be the point of intersection of the lines 3x + 2y = 14 and 5x - y = 6, and B be the point of intersection of the lines 4x + 3y = 8…

If x² - y² + 2hxy + 2gx + 2fy + c = 0 is the locus of a point that moves such that it is always equidistant from the lines x + 2y + 7 = 0…

Let A(a, b), B(3, 4), and C(-6, -8) denote the centroid, circumcenter, and orthocenter of a triangle. The distance of the point P(2a+3,…

Let a variable line passing through the center of the circle x² + y² - 16x - 4y = 0 meet the positive coordinate axes at points A and B.…

A ray of light coming from P(1, 2) reflects from Q on the x-axis and passes through R(4, 3). If S(h, k) makes PQRS a parallelogram, then…

A triangle is formed by the X-axis, Y-axis, and the line 3x + 4y = 60. Then the number of points P(a, b), where a is an integer and b is a…

A light ray emits from the origin making an angle of 30^° with the positive x-axis. After getting reflected by the line x + y = 1, if this…

A straight line cuts off the intercepts OA = a and OB = b on the positive directions of the x-axis and y-axis, respectively. If the…

Let the equations of two adjacent sides of a parallelogram ABCD be 2x - 3y = -23 and 5x + 4y = 23. \text{If the equation of its one…

Let R be a rectangle given by the lines x = 0, x = 2, y = 0 and y = 5. Let A(α, 0) and B(0, β), with α ∈ [0, 2] and β ∈ [0, 5], be such…

If the line l₁: 3y - 2x = 3 is the angular bisector of the line l₂: x - y + 1 = 0 and l₃: α x + β y + 17 = 0, then α² + β² - α - β is equal…