(A) Let the coordinates of $A$ be $(a, 0)$ and $B$ be $(0, b)$.Since $(x_1, y_1)$ is the midpoint of $AB$,we have $x_1 = \frac{a+0}{2} = \frac{a}{2}$

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(A) Let the coordinates of $A$ be $(a, 0)$ and $B$ be $(0, b)$.Since $(x_1, y_1)$ is the midpoint of $AB$,we have $x_1 = \frac{a+0}{2} = \frac{a}{2}$ and $y_1 = \frac{0+b}{2} = \frac{b}{2}$.This implies $a = 2x_1$ and $b = 2y_1$.The intercept form of the equation of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values of $a$ and $b$,we get $\frac{x}{2x_1} + \frac{y}{2y_1} = 1$.Multiplying both sides by $2x_1y_1$,we obtain $x y_1 + y x_1 = 2x_1y_1$.

Class 11 Mathematics Straight Line Slope of line, Equation of line in different forms

Medium

$A$ line meets the $x$-axis and $y$-axis at the points $A$ and $B$ respectively. If the midpoint of $AB$ is $(x_1, y_1)$,then the equation of the line is:

A
$y_1x + x_1y = 2x_1y_1$
B
$x_1x + y_1y = 2x_1y_1$
C
$y_1x + x_1y = x_1y_1$
D
$x_1x + y_1y = x_1y_1$

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Class 11

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Straight Line

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Slope of line, Equation of line in different forms

The equation of the line which passes through the point $(-4, 3)$ and whose portion intercepted between the axes is divided internally in the ratio $5 : 3$ by this point is:

Medium

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Points $A$ and $B$ are in the first quadrant; point $O$ is the origin. If the slope of $OA$ is $1$,the slope of $OB$ is $7$,and $OA = OB = r$,then the slope of $AB$ is:

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Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $y$-intercept is $-\frac{3}{2}$.

Easy

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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:

MediumIIT 1986

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$A$ line $L$ is perpendicular to the line $5x - y = 1$ and the area of the triangle formed by the line $L$ and the coordinate axes is $5$. The equation of the line $L$ is

EasyIIT 1980

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$A$ line meets the $x$-axis and $y$-axis at the points $A$ and $B$ respectively. If the midpoint of $AB$ is $(x_1, y_1)$,then the equation of the line is:

Similar Questions

The equation of the line which passes through the point $(-4, 3)$ and whose portion intercepted between the axes is divided internally in the ratio $5 : 3$ by this point is:

Points $A$ and $B$ are in the first quadrant; point $O$ is the origin. If the slope of $OA$ is $1$,the slope of $OB$ is $7$,and $OA = OB = r$,then the slope of $AB$ is:

Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $y$-intercept is $-\frac{3}{2}$.

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