Exams › JEE Main › Maths

A square has one diagonal lying on the line x = 2y. If one of its vertices is at (3, 0), then the equations of the two sides passing through this vertex are

1. y - 3x + 9 = 0, 3y + x - 3 = 0
2. y + 3x + 9 = 0, 3y + x - 3 = 0
3. y - 3x + 9 = 0, 3y - x + 3 = 0
4. y - 3x + 3 = 0, 3y + x + 9 = 0

Correct answer: y - 3x + 9 = 0, 3y + x - 3 = 0

Solution

The diagonal x=2y has slope 1/2; the sides through a vertex make 45 degrees with it, giving slopes (1/2+1)/(1-1/2)=3 and (1/2-1)/(1+1/2)=-1/3. Through (3,0): y-3x+9=0 and 3y+x-3=0 (these are perpendicular, as required).

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 →