Exams › JEE Main › Maths

For the pair of straight lines represented by my² + (1-m²)xy - mx² = 0, if one line is an angle bisector of the two coordinate axes given by xy = 0, then the value of m is

1. 1
2. 2
3. -1/2
4. -2

Correct answer: 1

Solution

The given equation represents two straight lines, and for one of them to be an angle bisector of the coordinate axes, it must have a slope of 1 or -1. Substituting m = 1 into the equation results in one of the lines having a slope of 1, confirming that it bisects the angle between the axes.

Related JEE Main Maths questions

• Consider the following statements: Statement 1: The greatest possible number of intersection points formed by 8 circles of the same radius is 56. Statement 2: The greatest possible number of points of intersection obtained when 4 circles of different radii and 4 distinct straight lines are drawn is 50.
• Find the length of the segment from the point (1, 2) to the line x + y + 5 = 0, if the measurement is taken along a line parallel to 3x − y = 7.
• Let p1 and p2 denote the perpendicular distances from the origin to the lines x cos θ + y sin θ = 2a cos 4θ and x sec θ + y cosec θ = 4a cos 2θ, respectively. If mp1² + np2² = 4a², then which of the following is true?
• For which value of p² does the equation y² + xy + px² − x − 2y + p = 0 represent a pair of straight lines?
• An equilateral triangle has one vertex at (2, 3). If the side opposite to this vertex lies on the line x + y = 2, then the equations of the other two sides are
• Which points on the line x + y = 4 are exactly one unit away from the line 4x + 3y = 10?

⚔️ Practice JEE Main Maths free + battle 1v1 →