Question

The line $(5x-8y+11)\lambda +(8x-3y+4)=0$

is parallel to X-axis. Find $\lambda$.

Answer 1

The given line is

$(5x-8y+11)\lambda +(8x-3y+4)=0$

That is, $x(5\lambda +8)-y(8\lambda +3)+(11\lambda +4)=0$

As the given line is parallel to X-axis, its slope = 0, i.e.,

$\frac{-(5\lambda +8)}{-(8\lambda +3)}=0$

$5\lambda +8=0$

Hence, $\lambda =-\frac{8}{5}$.