Question

If the line ${\displaystyle \frac{x}{\text{a}}+\frac{y}{\text{b}}}$ = 1 passes through the points (2, –3) and (4, –5), then (a, b) is ______.

Options

• (1, 1)

• (– 1, 1)

• (1, – 1)

• (– 1, –1)

Answer 1

If the line ${\displaystyle \frac{x}{\text{a}}+\frac{y}{\text{b}}}$ = 1 passes through the points (2, –3) and (4, –5), then (a, b) is (– 1, –1).

Explanation:

Equation of line passing through the points (2, – 3) and (4, – 5) is y + 3 = ${\displaystyle \frac{-5+3}{4-2}(x-2)}$

⇒ y + 3 = ${\displaystyle \frac{-2}{2}(x-2)}$

⇒ y + 3 = – (x – 2)

⇒ y + 3 = – x + 2

⇒ x + y = – 1

⇒ ${\displaystyle \frac{x}{-1}+\frac{y}{-1}}$ = 1   (Intercept form)

∴ a = – 1, b = – 1