If the line \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1 passes through the p

1.	If the line \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1 passes through the point (2, – 3) and (4, – 5), find the a and b.
Answer» Equation of a line in intercept form is \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1 …(1) Since the line passes through (2, 3) and (4, – 5). ∴ \(\frac{2}{a}\) − \(\frac{3}{b}\) = 1 ⇒ 2p − 3q = 1 …(2) [let \(\frac{1}{a}\) = p, \(\frac{1}{b}\) = q] And \(\frac{4}{a}\) − \(\frac{5}{b}\) = 1 ⇒ 4p − 5q = 1 …(3) (2) and (3) ⇒ p = – 1, q = – 1. ∴ a = – 1, b = – 1.

If the line \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1 passes through the point (2, – 3) and (4, – 5), find the a and b.

Answer»

Equation of a line in intercept form is \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1 …(1)

Since the line passes through (2, 3) and (4, – 5).

∴ \(\frac{2}{a}\) − \(\frac{3}{b}\) = 1 ⇒ 2p − 3q = 1 …(2)

[let \(\frac{1}{a}\) = p, \(\frac{1}{b}\) = q]

And \(\frac{4}{a}\) − \(\frac{5}{b}\) = 1 ⇒ 4p − 5q = 1 …(3)

(2) and (3) ⇒ p = – 1, q = – 1.

∴ a = – 1, b = – 1.