Find the equation of the line passing through | vedclass

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

Question

(A) Let the equation of the line having equal intercepts on the axes be $\frac{x}{a} + \frac{y}{a} = 1$,which simplifies to $x + y = a$ ......$(1)$.To

Vedclass · Accepted Answer

$13x + 13y = 6$

Vedclass · Answer

(A) Let the equation of the line having equal intercepts on the axes be $\frac{x}{a} + \frac{y}{a} = 1$,which simplifies to $x + y = a$ ......$(1)$.To find the point of intersection,solve the system of equations:$4x + 7y = 3$ ......$(2)$$2x - 3y = -1$ ......$(3)$Multiplying equation $(3)$ by $2$,we get $4x - 6y = -2$ ......$(4)$.Subtracting $(4)$ from $(2)$ gives $(4x + 7y) - (4x - 6y) = 3 - (-2)$,which implies $13y = 5$,so $y = \frac{5}{13}$.Substituting $y = \frac{5}{13}$ into $(3)$,$2x - 3(\frac{5}{13}) = -1 \Rightarrow 2x = \frac{15}{13} - 1 = \frac{2}{13}$,so $x = \frac{1}{13}$.The point of intersection is $(\frac{1}{13}, \frac{5}{13})$.Since the line $x + y = a$ passes through $(\frac{1}{13}, \frac{5}{13})$,we have $\frac{1}{13} + \frac{5}{13} = a$,which gives $a = \frac{6}{13}$.Substituting $a$ into equation $(1)$,we get $x + y = \frac{6}{13}$,or $13x + 13y = 6$.

Find the equation of the line passing through the point of intersection of the lines $4x + 7y - 3 = 0$ and $2x - 3y + 1 = 0$ that has equal intercepts on the axes.

Similar Questions

The intercept cut off from the $y$-axis is twice that from the $x$-axis by a line,and the line passes through $(1, 2)$. Find its equation.

The minimum area of the triangle formed by the variable line $3 \cos \theta \cdot x + 4 \sin \theta \cdot y = 12$ and the coordinate axes is

One diagonal of a square is along the line $8x - 15y = 0$ and one of its vertices is $(1, 2)$. Then the equations of the sides of the square passing through this vertex are:

The equation of the line bisecting the join of $(3, -4)$ and $(5, 2)$ and having its intercepts on the $x$-axis and the $y$-axis in the ratio $2 : 1$ is

The equations of lines parallel to the coordinate axes and passing through the point $(5, -6)$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module