Question

If $\frac{1}{a{b}^{\prime }}+\frac{1}{b{a}^{\prime }}$ = 0, then lines $\frac{x}{b^{\prime }}+\frac{y}{a^{\prime }}$ and $\frac{x}{a}+\frac{y}{b}$ = 1 are ___________________

• A. Parallel lines
• B. Inclined at 60⁰ to each other
• C. Perpendicular to each other
• D. Inclined at 30⁰ to each other

Answer 1

The correct option is C

Perpendicular to each other

Lines are $\frac{x}{a}+\frac{y}{b}=1$ bx + ay - ab=0 ........(1)
$\frac{x}{b^{\prime }}+\frac{y}{a^{\prime }}=1$
a'x + b'y - a'b' = 0
From the given condition ........(2)
$\frac{1}{a{b}^{\prime }}+\frac{1}{b{a}^{\prime }}=0$
a'b + b'a = 0
a'b = b'a
$\frac{a^{\prime }b}{a{b}^{\prime }}=-1$
$\left(\frac{-b}{a}\right).\left(\frac{-a^{\prime }}{b^{\prime }}\right)=-1$

Slope of line 1 x slope of line 2
$m_1.m_2=-1$
So, we can say that these two lines are perpendicular to each other.