Question

$k$ is a nonzero constant. If $k=\frac{a+b}{ab}$ then the straight line $\frac{x}{a}+\frac{y}{b}=1$ passes through the point

• A. $(k,k)$
• B. $(1/k,1/k)$
• C. $(1,1)$
• D. $(k,1/k)$

Answer 1

Answer: (B)

$(1/k,1/k)$

We have,

$k=\frac{a+b}{ab}$

$\Rightarrow a+b=kab.......\left(1\right)$

And

$\frac{x}{a}+\frac{y}{b}=1$

$\Rightarrow bx+ay=ab$

$\Rightarrow ay+bx=ab.......\left(2\right)$

Form equation (1) and (2) to, and we get,

$\frac{1}{y}=\frac{1}{x}=\frac{k}{1}$

So,

$x=\frac{1}{k},x=\frac{1}{k}$

So,

$(x,y)=(\frac{1}{k},\frac{1}{k})$

Hence, this is the answer.