Straight LineHardBloom L3
Question
If the line $y = x$ is one of the angle bisector of the pair of lines $ax^{2} + 2hxy + by^{2} = 0$, then:
Options
A.$a + b = 0$
B.$a - b = 0$
C.$h = 0$
D.$a + 2b = 0$
Solution
Sol. [Key Concept: $y = x$ being an angle bisector of ${ax}^{2 + 2}hxy + {by}^{2 = 0}$ forces $a + b = 0$.]
Lines make complementary angles with $X$-axis $\Rightarrow m_{1}m_{2} = 1 \Rightarrow \frac{a}{b} = 1$
Create a free account to view solution
View Solution FreeMore Straight Line Questions
A line passes through the point (1, 2) and makes 60o angle with x axis. A point on this line at a distance 3 from the po...Two straight lines $u = 0$ and $v = 0$ passes through the origin and the angle between them is $\tan^{- 1}\left( \frac{7...The straight line L is perpendicular to the line 5x − y = 1. The area of the triangle formed by the line L and coo...The point (a2, a + 1) lies in the angle between the lines 3x − y + 1 = 0 and x + 2y − 5 = 0 containing the o...A straight line L through the point (3, - 2) is inclined at an angle 60o to the line √3x + y = 1. If L also inters...