Choose the correct answer. If the line x a + y b =1 passes throug… - Vidyadip

MCQ

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

A
(1, 1)
B
(-1, 1)
C
(1, -1)
✓
(-1, -1)

✓

Answer

Correct option: D.

(-1, -1)

Equation of line passing through the points (2, -3) and (4, -5) is
$\text{y}+3=\frac{-5+3}{4-2}(\text{x}-2)$
$\Rightarrow \text{y}+3=\frac{-2}{2}(\text{x}-2)$
$\Rightarrow \text{y}+3=-(\text{x}-2)$
$\Rightarrow \text{y}+3=-\text{x}+2$
$\Rightarrow \text{x}+\text{y}=-1$
$\Rightarrow \frac{\text{x}}{-1}+\frac{\text{y}}{-1}=1$ (intercept from)
$\therefore \text{a}=-1,\text{b}=-1$
Hence, the correct option is (d).

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