Question

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

• A. $(1,1)$
• B. $(-1,1)$
• C. $(1,-1)$
• D. $(-1,-1)$

Answer 1

Answer: (D)

Given line is $\frac{x}{a}+\frac{y}{b}=1\dots \left(i\right)$
Now, $\left(i\right)$ passes through $\left(2,-3\right)$ and $\left(4,-5\right)$
$\therefore \left(2,-3\right)$ and $\left(4,-5\right)$ satisfies it
So, $\frac{2}{a}-\frac{3}{b}=1\dots \left(ii\right)$ and
$\frac{4}{a}-\frac{5}{b}=1\dots \left(iii\right)$
On solving $\left(ii\right)$ and $\left(iii\right)$,
we get $a=-1$, $b=-1$