Question

The equations of two lines through $( 0 , a )$which are at distance ‘a’ from the point $( 2 a , 2 a )$ are.

• A. $y - a = 0$ and $4 x - 3 y - 3 a = 0$
• B. $y - a = 0$ and $3 x - 4 y + 3 a = 0$
• C. $y - a = 0$ and $4 x - 3 y + 3 a = 0$
• D. None of these

Answer 1

Answer: (C)

$y - a = 0$ and $4 x - 3 y + 3 a = 0$

Answer 2

Equation of any line through $( 0 , a )$is

$y - a = m ( x - 0 )$ or $m x - y + a = 0$ …..(i)

If the length of perpendicular from (2a, 2a) to the line (i) is ‘a’, then $a = \pm \frac { m ( 2 a ) - 2 a + a } { \sqrt { m ^ { 2 } + 1 } } \Rightarrow m = 0 , \frac { 4 } { 3 }$.

Hence the required equations of lines are $y - a = 0$ $4 x - 3 y + 3 a = 0$.