Question

The equation of straight line passing through point of intersection of the straight lines $3 x - y + 2 = 0$ and $5 x - 2 y + 7 = 0$ and having infinite slope is

• A. $x = 2$
• B. $x + y = 3$
• C. $x = 3$
• D. $x = 4$

Answer 1

Answer: (C)

$x = 3$

Answer 2

Required line should be, $( 3 x - y + 2 ) + \lambda ( 5 x - 2 y + 7 ) = 0$.....(i)

⇒ $( 3 + 5 \lambda ) x - ( 2 \lambda + 1 ) y + ( 2 + 7 \lambda ) = 0$

⇒ $y = \left( \frac { 3 + 5 \lambda } { 2 \lambda + 1 } \right) x + \frac { 2 + 7 \lambda } { 2 \lambda + 1 }$ ......(ii)

As the equation (ii) has infinite slope, $2 \lambda + 1 = 0$ ⇒ $\lambda = \frac { - 1 } { 2 }$

Putting $\lambda = \frac { - 1 } { 2 }$ in equation (i), We have

$( 3 x - y + 2 ) + \left( \frac { - 1 } { 2 } \right) ( 5 x - 2 y + 7 ) = 0$ ⇒ $x = 3$