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

Question

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 (A)  2 x + 3 y = ± √5 (B)  x + y = ± 2 (C)  x - y = ± 2 (D)  2 x + y = ± √5

Tardigrade Admin · Accepted Answer

Let equation of line be (x/a)+(y/2 a)=1 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/dc9ac3b611e074d97115185458e60f02-.png" /> ⇒ 2 x+y=2 a Distance from origin is |(2 a/√(2)2+(1)2)|=|(2 a/√5)| ⇒ |(2 a/√5)|=1 ⇒ 2 a=± √5 Hence, equation of line is 2 x+y=± √5

Q. $A$ 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

$2 x + 3 y = \pm 5$

$x + y = \pm 2$

$x - y = \pm 2$

$2 x + y = \pm 5$

Q. 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

2x+3y=±5​

x+y=±2

x−y=±2

2x+y=±5​

Let equation of line be ax​+2ay​=1 ⇒2x+y=2a Distance from origin is ∣∣​(2)2+(1)2​2a​∣∣​=∣∣​5​2a​∣∣​ ⇒∣∣​5​2a​∣∣​=1 ⇒2a=±5​ Hence, equation of line is 2x+y=±5​

Q. $A$ 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

$2 x + 3 y = \pm 5$

$x + y = \pm 2$

$x - y = \pm 2$

$2 x + y = \pm 5$