Find the equation of a line which is bisected | vedclass

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

Question

(A) Let the equation of the line in intercept form be $\frac{x}{a} + \frac{y}{b} = 1$.The coordinates of the points where the line intersects the $x$-

Vedclass · Accepted Answer

$\frac{x}{x_1} + \frac{y}{y_1} = 2$

Vedclass · Answer

(A) Let the equation of the line in intercept form be $\frac{x}{a} + \frac{y}{b} = 1$.The coordinates of the points where the line intersects the $x$-axis and $y$-axis are $(a, 0)$ and $(0, b)$ respectively.The midpoint of the segment intercepted between the axes is $(\frac{a}{2}, \frac{b}{2})$.Given that the line is bisected at $(x_1, y_1)$,we have $\frac{a}{2} = x_1 \implies a = 2x_1$ and $\frac{b}{2} = y_1 \implies b = 2y_1$.Substituting these values into the intercept form equation:$\frac{x}{2x_1} + \frac{y}{2y_1} = 1$Multiplying by $2$,we get $\frac{x}{x_1} + \frac{y}{y_1} = 2$.

Find the equation of a line which is bisected at the point $(x_1, y_1)$ by the axes.

Similar Questions

Find the value of $k$,if the line joining the points $(2, k)$ and $(3, 7)$ is parallel to the line joining points $(-2, 1)$ and $(3, 0)$.

$A$ line passing through the point $A(2, 3)$ makes an angle of $45^{\circ}$ with the $x$-axis and intersects the line $x + y + 1 = 0$ at point $P$. Find the distance $AP$.

Find the number of integer values of $m$ such that the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is an integer.

The system of linear equations $ax - y + 2 = 0$ and $x + ay + 3 = 0$ has a unique solution. Then,the set of values of $a$ is . . . . . . .

If the three points $(3q, 0)$, $(0, 3p)$, and $(1, 1)$ are collinear, then which one is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module