Question

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

Answer 1

$$\begin{gathered} \mathrm{Since}\frac{x}{a}+\frac{y}{b}=1\mathrm{is}\mathrm{the}\mathrm{given}\mathrm{line}\mathrm{which}\mathrm{passes}\mathrm{through}(2,-3)\mathrm{and}(4,-5) \\ \mathrm{i}.\mathrm{e}.\frac{2}{a}-\frac{3}{b}=1\mathrm{and}\frac{4}{a}-\frac{5}{b}=1 \\ \mathrm{i}.\mathrm{e}.\frac{4}{a}-\frac{6}{b}=2\mathrm{and} \\ \begin{array}{cccccc}& \frac{4}{a}& -& \frac{5}{b}& =& 1\\ & -& +& & -& \\ & & & \frac{-1}{b}& =& 1\end{array} \\ \mathrm{i}.\mathrm{e}.b=-1 \\ \therefore \frac{4}{a}+5=1 \\ \mathrm{i}.\mathrm{e}.\frac{4}{a}=-4 \\ \mathrm{i}.\mathrm{e}.a=-1 \end{gathered}$$
i.e. (a, b) = (–1, –1)

Hence, the correct answer is option D.