The equation of the line perpendicular to the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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

Similar Questions

Find the equation of a line that makes an angle of $60^{\circ}$ with the $x$-axis and makes an intercept of $5$ units on the negative direction of the $y$-axis.

The equations of the lines which cut off an intercept of $-1$ from the $y$-axis and are equally inclined to the axes are

If $x \cos \alpha + y \sin \alpha = p$ is the normal form of the equation of a straight line $x + \sqrt{3} y + 4 = 0$ and $a, b$ are respectively $X$ and $Y$ intercepts of this line,then $\sqrt{3} \pi b p - 3 a \alpha = $

Find the general equation of a line perpendicular to $x + y + 4 = 0$ and passing through the point $(1, 2)$.

$A$ line is perpendicular to the line $ax + by + c = 0$ and passes through $(a, b)$. The equation of the line is

Vedclass Test Series

Exam Paper Generator

Online Exam Module