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…

Rhombus vertices A(1,2), C(-3,-6). Line AD parallel to 7x-y=14. Find | + + + |.

Let A(1,0), B(2,-1) and C ( 73, 43) be three points. If the equation of the bisector of the angle ABC is x+ y=5, then the value of ^2+ ^2 is

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 23…

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

Let the points ( 112,) lie on or inside the triangle with sides x + y = 11, x + 2y = 16, and 2x + 3y = 29. Then the product of the smallest…

If a = 1 + r=1^6 (-3)^r-1 122r-1, then the distance of the point (12, 3) from the line 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(3 + 1) + y(7 + 2) = 17 + 5. If P is the point through which all these lines pass and the distance of L from the point…

Let the equation x(x+2)(12-k) = 2 have equal roots. The distance of the point (k, k2) 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 with the positive x-axis. Let this line be rotated about the point P through…

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 (a^2, a + 1) lie in R:

The values of for which lines 2x - y + 3 = 0, 6x + 3y + 1 = 0, and x + 2y - 2 = 0 do not form a triangle are:

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

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 A…

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 x^2 - y^2 + 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 x^2 + y^2 - 16x - 4y = 0 meet the positive coordinate axes at points A and B.…

The values of for which lines 2x - y + 3 = 0, 6x + 3y + 1 = 0, and ax + 2y - 2 = 0 do not form a triangle are:

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. If the equation of its one diagonal AC…

Let R be a rectangle given by the line x = 0, x - 2y = 5. Let A(, 0) and B(0,) with [0,5] and [0, 5], be such that the line segment AB…

If the line l1: 3y - 2x = 3 is the angular bisector of the line l2: x - y + 1 = 0 and l3: x + y + 17 = 0, then ^2 + ^2 - - is equal to.