Question
Straight lines $2x + y = 5$ and $x - 2y = 3$ intersect at point $A$. Points $B$ and $C$ are chosen on these two lines such that $AB = AC$. Then the equation of a line $BC$ passing through the point $(2,3)$ is:
Options
Solution
Sol. [Key Concept: $AB = AC$ ⇒ $A$ lies on the bisector of the two lines; $BC$ is $\perp$ to that bisector through $(2,3)$.]
$BC$ is parallel to angle bisector of lines
$2x + y = 5$ and $x - 2y = 3$
$$\frac{2x + y - 5}{\sqrt{5}} = \pm \frac{x - 2y - 3}{\sqrt{5}} \Rightarrow x + 3y = c $$Eqn. of $BC$ can be $x + 3y = 11$
or
$$3x - y = 3$$
✔ (a) $3x - y - 3 = 0$ is a valid line through $(2,3)$.
✔ (b) $x + 3y - 11 = 0$ is the other valid line through $(2,3)$.
✘ (c) does not pass through $(2,3)$ with the required inclination.
✘ (d) does not satisfy the isosceles condition.
Create a free account to view solution
View Solution Free