The intercept of a line between the coordinat | vedclass

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

Question

(B) Let the intercepts of the line on the $x$-axis and $y$-axis be $a$ and $b$ respectively. The coordinates of the points are $A(a, 0)$ and $B(0, b)$

Vedclass · Accepted Answer

$8x - 5y + 60 = 0$

Vedclass · Answer

(B) Let the intercepts of the line on the $x$-axis and $y$-axis be $a$ and $b$ respectively. The coordinates of the points are $A(a, 0)$ and $B(0, b)$.Given that the point $P(-5, 4)$ divides the line segment $AB$ in the ratio $1 : 2$.Using the section formula,the coordinates of $P$ are given by $\left( \frac{1 \cdot 0 + 2 \cdot a}{1 + 2}, \frac{1 \cdot b + 2 \cdot 0}{1 + 2} \right) = \left( \frac{2a}{3}, \frac{b}{3} \right)$.Equating the coordinates,we get $\frac{2a}{3} = -5 \implies a = -\frac{15}{2}$ and $\frac{b}{3} = 4 \implies b = 12$.The intercept form of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values,we get $\frac{x}{-15/2} + \frac{y}{12} = 1 \implies -\frac{2x}{15} + \frac{y}{12} = 1$.Multiplying by $60$,we get $-8x + 5y = 60$,which simplifies to $8x - 5y + 60 = 0$.

The intercept of a line between the coordinate axes is divided by the point $(-5, 4)$ in the ratio $1 : 2$. The equation of the line will be:

Similar Questions

The line passing through the points $(a, b)$ and $(-a, -b)$ passes through which of the following points?

The line $(3x - y + 5) + \lambda (2x - 3y - 4) = 0$ will be parallel to the $y$-axis,if $\lambda$ =

The sum of the squares of the intercepts made by the line $5x - 2y = 10$ on the coordinate axes equals:

The equation of the straight line passing through $(-a, 0)$ and forming a triangle with the coordinate axes of area $T$ is

The equation of the line,passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \cos \theta - y \sin \theta = a$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module