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Family of Straight Lines

The family of...

Question

The family of lines $x (a + b) + y (a - b) = 2 a, a, b \in R$ are concurrent at $(p, q)$ then the value of $p + q$ is

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Solution

Given line $x (a + b) + y (a - b) = 2 a$
$\Rightarrow a (x + y - 2) + b (x - y) = 0$
$\Rightarrow (x + y - 2) + \frac{b}{a} (x - y) = 0$
This is a family of lines concurrent at point of intersection of lines $x - y = 0$ and $x + y - 2 = 0$ .
On solving these two equations we get $(p, q) \equiv (1, 1) ∴ p + q = 2$

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Family of Straight Lines

Standard XII Mathematics

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