Exams › JEE Advanced › Maths
Find the equation of the bisector of the acute angle between the lines x + 2y - 11 = 0 and 3x - 6y - 5 = 0 that contains the point (1, -3).
- 3x = 19
- 3y = 7
- 3x = 19 and 3y = 7
- None of these
Correct answer: 3x = 19
Solution
The two angle bisectors are found from (x+2y-11)/sqrt(5) = +/-(3x-6y-5)/(3*sqrt(5)). The positive case gives 3y=7 and the negative case gives 3x=19. At (1,-3): L1 = 1+2(-3)-11 = -16 < 0 and L2 = 3-6(-3)-5 = 16 > 0. Since L1 and L2 have opposite signs at the point, the bisector through that angular region comes from the negative-sign equation, which is 3x=19.
Related JEE Advanced Maths questions
- Determine the range of β for which the point (0, β) is located on or within the triangle formed by the equations y + 3x + 2 = 0, 3y − 2x − 5 = 0, and 4y − x − 14 = 0.
- For the equation a² + b² − c² − 2ab = 0, the common intersection point of the set of lines represented by ax + by + c = 0 is located on which line?
- If the points (a³/(a − 3), (a² − 3)/(a − 1)), (b³/(b − 3), (b² − 3)/(b − 1)), and (c³/(c − 3), (c² − 3)/(c − 1)), where a, b, and c are not equal to 1, are situated on the line l₁x + m₁y + n₁ = 0, then which of the following is true?
- In triangle ABC, the median AD is divided into two equal parts at point E. Line BE intersects AC at point F. What is the ratio of AF to AC?
- Let m1 and m2 be the slopes of two adjacent sides of a square of side length a such that a² + 11a + 3(m1² + m2²) = 220. One vertex of the square is at the point (10(cos(alpha) - sin(alpha)), 10(sin(alpha) + cos(alpha))), where alpha is in (0, pi/2), and one diagonal of the square has equation (cos(alpha) - sin(alpha))x + (sin(alpha) + cos(alpha))y = 10. Find the value of 72(sin⁴(alpha) + cos⁴(alpha)) + a² - 3a + 13.
- Let P be any point on the line x - y + 3 = 0 and let A = (3, 4) be a fixed point. A family of lines given by (3 sec(t) + 5 cosec(t)) x + (7 sec(t) - 3 cosec(t)) y + 11(sec(t) - cosec(t)) = 0 passes through a fixed point B for all permissible values of t. If the maximum value of |PA - PB| is expressed as 2 * sqrt(2n) where n is a natural number, find n.
⚔️ Practice JEE Advanced Maths free + battle 1v1 →