Question

The number of lines that are parallel to $2 x + 6 y + 7 = 0$ and have an intercept of length 10 between the coordinate axes is.

• A. 1
• B. 2
• C. 4
• D. Infinitely many

Answer 1

Answer: (B)

2

Answer 2

The equation of any line parallel to $2 x + 6 y + 7 = 0$ is $2 x + 6 y + k = 0$ .

This meets the axes at $A \left( - \frac { k } { 2 } , 0 \right)$and $B \left( 0 , - \frac { k } { 6 } \right)$ .

By hypothesis, $A B = 10$

$\Rightarrow \sqrt { \frac { k ^ { 2 } } { 4 } + \frac { k ^ { 2 } } { 36 } } = 10 \Rightarrow \sqrt { \frac { 10 k ^ { 2 } } { 36 } } = 10$

⇒ $10 k ^ { 2 } = 3600 \Rightarrow k = \pm 6 \sqrt { 10 }$.

Hence there are two lines given by $2 x + 6 y \pm 6 \sqrt { 10 } = 0$.