Question

If a straight line is perpendicular to $2x+8y=10$ and meets the $x$-axis at $(5,0)$, then it meets the $y$-axis at

• A. $(0,-2)$
• B. $(0,-8)$
• C. $(0,-10)$
• D. $(0,-16)$
• E. $(0,-20)$

Answer 1

The correct option is E $(0,-20)$

Let the slope of the line be $m$.
Slope of the line $2x+8y=10$ is
$\frac{-2}{8}=-\frac{1}{4}$
Since, both the lines are perpendicular.
Therefore, $m=\frac{-1}{(-\frac{1}{4})}=4$
Hence, equation of the required line will be $y=4x+c$.
It is given that, above line pass through $(5,0)$.
Then, $0=4\times 5+c$
$\Rightarrow c=-20$
So, the line will intersect the $y$-axis at $(0,-20)$.