Straight Line and Pair of Straight Lines 3 Question 9
10. The set of lines $a x+b y+c=0$, where $3 a+2 b+4 c=0$ is concurrent at the point… .
$(1982,2 M)$
True/False
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Answer:
Correct Answer: 10. $\frac{3}{4}, \frac{1}{2}$
Solution:
- The set of lines $a x+b y+c=0$, where $3 a+2 b+4 c=0$ or $\frac{3}{4} a+\frac{1}{2} b+c=0$ are concurrent at $x=\frac{3}{4}, y=\frac{1}{2}$ i.e. comparing the coefficients of $x$ and $y$.
Thus, point of concurrency is $\frac{3}{4}, \frac{1}{2}$.
Alternate Solution
As, $\quad a x+b y+c=0, \quad$ satisfy $\quad 3 a+2 b+4 c=0 \quad$ which represents system of concurrent lines whose point of concurrency could be obtained by comparison as,
$$ a x+b y+c \equiv \frac{3 a}{4}+\frac{2}{4} b+c $$
$\Rightarrow \quad x=\frac{3}{4}, y=\frac{1}{2}$ is point of concurrency.
$\therefore \quad \frac{3}{4}, \frac{1}{2}$ is the required point.
