The equation of the line perpendicular to the | vedclass

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(D) The given line is $\frac{x}{a} - \frac{y}{b} = 1$,which can be written as $bx - ay = ab$.The line cuts the $x$-axis where $y = 0$. Substituting $y

Vedclass · Accepted Answer

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

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(D) The given line is $\frac{x}{a} - \frac{y}{b} = 1$,which can be written as $bx - ay = ab$.The line cuts the $x$-axis where $y = 0$. Substituting $y = 0$ in the equation,we get $bx = ab$,so $x = a$. Thus,the point of intersection is $(a, 0)$.The slope of the given line $bx - ay = ab$ is $m_1 = \frac{b}{a}$.The slope of the line perpendicular to it is $m_2 = -\frac{1}{m_1} = -\frac{a}{b}$.The equation of the line with slope $m_2 = -\frac{a}{b}$ passing through $(a, 0)$ is $y - 0 = -\frac{a}{b}(x - a)$.Multiplying by $b$,we get $by = -ax + a^2$,which simplifies to $ax + by = a^2$.Dividing both sides by $ab$,we get $\frac{ax}{ab} + \frac{by}{ab} = \frac{a^2}{ab}$,which results in $\frac{x}{b} + \frac{y}{a} = \frac{a}{b}$.

The equation of the line perpendicular to the line $\frac{x}{a} - \frac{y}{b} = 1$ and passing through the point at which it cuts the $x$-axis,is

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