$A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
- $ 2\,x + 3\,y = \pm \sqrt{5}$
- $ x + y = \pm 2$
- $ x - y = \pm 2$
- $ 2\,x + y = \pm \sqrt{5}$
The Correct Option is D
Solution and Explanation
$\frac{x}{a}+\frac{y}{2 a}=1$
$\Rightarrow 2 \,x+y=2\,a$
Distance from origin is
$\left|\frac{2 a}{\sqrt{(2)^{2}+(1)^{2}}}\right|=\left|\frac{2 a}{\sqrt{5}}\right| $
$\Rightarrow \left|\frac{2 a}{\sqrt{5}}\right|=1 $
$\Rightarrow 2 \,a=\pm \sqrt{5}$
Hence, equation of line is $2\, x+y=\pm \sqrt{5}$
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Concepts Used:
x-intercepts and y-intercepts
Intercept:
The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.
The meaning of intercept of a line is the point at which it intersects either the x-axis or y-axis.
X- intercept
The x-intercept represents where the graph crosses the x-axis. The x-intercept of a line gives the idea about the point which crosses the x-axis.
Y-intercept
The y-intercept represents where the graph crosses the y-axis. The y-intercept is a point at which the line crosses the y-axis.
X and Y Intercept Formula:
The x-intercept of a line is the point at which the line crosses the x axis. ( i.e. where the y value equals 0 )
X - intercept = (x, 0)
The y-intercept of a line is the point at which the line crosses the y axis. ( i.e. where the x value equals 0 )
Y - intercept = (0, y)