Find the equations of the lines parallel to the axes and passing through the point $(-2, 3)$.
(N/A) The position of the lines is shown in the figure.
For a line parallel to the $x$-axis,the $y$-coordinate of every point on the line remains constant. Since the line passes through $(-2, 3)$,the $y$-coordinate is $3$. Therefore,the equation of the line parallel to the $x$-axis is $y = 3$.
Similarly,for a line parallel to the $y$-axis,the $x$-coordinate of every point on the line remains constant. Since the line passes through $(-2, 3)$,the $x$-coordinate is $-2$. Therefore,the equation of the line parallel to the $y$-axis is $x = -2$.
For a line parallel to the $x$-axis,the $y$-coordinate of every point on the line remains constant. Since the line passes through $(-2, 3)$,the $y$-coordinate is $3$. Therefore,the equation of the line parallel to the $x$-axis is $y = 3$.
Similarly,for a line parallel to the $y$-axis,the $x$-coordinate of every point on the line remains constant. Since the line passes through $(-2, 3)$,the $x$-coordinate is $-2$. Therefore,the equation of the line parallel to the $y$-axis is $x = -2$.
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Match the items given in List-$I$ to the items given in List-$II$. List-$I$ List-$II$ $A$. Line passing through $(-4, 3)$ and having intercepts in the ratio $5:3$ $1$. $2x - 5y + 4 = 0$ $B$. Line passing through $P(2, -5)$ such that $P$ bisects the part intercepted between the axes $2$. $3x + 5y = 3$ $C$. Line parallel to $2x - 3y + 5 = 0$ with $x$-intercept $\frac{2}{5}$ is $3$. $10x - 15y + 4 = 0$ $D$. Line perpendicular to $5x + 2y + 7 = 0$ with $y$-intercept $\frac{4}{5}$ is $4$. $10x - 15y = 4$ $5$. $5x - 2y - 20 = 0$
| List-$I$ | List-$II$ |
| $A$. Line passing through $(-4, 3)$ and having intercepts in the ratio $5:3$ | $1$. $2x - 5y + 4 = 0$ |
| $B$. Line passing through $P(2, -5)$ such that $P$ bisects the part intercepted between the axes | $2$. $3x + 5y = 3$ |
| $C$. Line parallel to $2x - 3y + 5 = 0$ with $x$-intercept $\frac{2}{5}$ is | $3$. $10x - 15y + 4 = 0$ |
| $D$. Line perpendicular to $5x + 2y + 7 = 0$ with $y$-intercept $\frac{4}{5}$ is | $4$. $10x - 15y = 4$ |
| $5$. $5x - 2y - 20 = 0$ |
The equation of the line parallel to the line $2x - 3y = 1$ and passing through the midpoint of the line segment joining the points $(1, 3)$ and $(1, -7)$ is:
Easy
View Solution$a$ and $b$ are the intercepts made by a line on the coordinate axes. If $3a = b$ and the line passes through $(1, 3)$,then the equation of the line is
The $y$-intercept made by the line $x \cos \alpha + y \sin \alpha = a$ is:
Easy
View SolutionThe equation of a line perpendicular to $x = c$ is
Medium
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