Straight LineHardBloom L3
Question
In the adjacent figure $\bigtriangleup ABC$ is right angled at $B$. If $AB = 4$ and $BC = 3$ and side $AC$ slides along the coordinate axes in such a way that ' $B$ ' always remains in the first quadrant, then $B$ always lie on straight line:
Options
A.$y = x$
B.$3y = 4x$
C.$4y = 3x$
D.$x + y = 0$
Solution
Sol. [Key Concept: Right angle at $B$ with legs of fixed length sliding on the axes ⇒ $B$ traces the line $y = \frac{BC}{AB}x$.]
$tan\theta = \frac{3}{4}\ $ (from Fig.)
⇒ Slope of $OB = tan\left( \frac{\pi}{2} - \theta \right) = cot\theta$
⇒ Locus of $(h,k)$ is $\frac{k}{h} = \frac{4}{3}$
$$\Rightarrow 3y = 4x$$
Create a free account to view solution
View Solution FreeMore Straight Line Questions
$A,B$ and $C$ are points in the $xy$-plane such that $A(1,2);B(5,6)$ and $AC = 3BC$. Then :...A straight line L through the point (3, − 2) is inclined at an angle of 60o to the line 3 x + y = 1. If L also int...The angle between the lines represented by the equation λx2 + (1 − λ)2 xy − λy2 = 0 is -...Area of the parallelogram formed by the lines y = mx, y = mx +1, y = nx and y = nx +1 equals...If one diagonal of a square is the portion of line $\frac{x}{a} + \frac{y}{b} = 1$ intercepted by the axes, then the ext...