SATHEE: Straight Line and Pair of Straight Lines 3 Question 9

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

Show Answer

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, $a x + b y + c = 0,$ satisfy $3 a + 2 b + 4 c = 0$ which represents system of concurrent lines whose point of concurrency could be obtained by comparison as,

$a x + b y + c \equiv \frac{3 a}{4} + \frac{2}{4} b + c$

$\Rightarrow x = \frac{3}{4}, y = \frac{1}{2}$ is point of concurrency.

$∴ \frac{3}{4}, \frac{1}{2}$ is the required point.

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Straight Line and Pair of Straight Lines 3 Question 9

10. The set of lines ax+by+c=0, where 3a+2b+4c=0 is concurrent at the point… .

True/False

Answer:

Alternate Solution

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10. The set of lines $a x + b y + c = 0$ , where $3 a + 2 b + 4 c = 0$ is concurrent at the point… .