Question

The line perpendicular to $4x-5y+1=0$ and passing through the point of intersection of the straight line $x+2y-10=0$ and $2x+y+5=0$ is ?

• A. $y+\dfrac{5x}{4}=\dfrac{50}{3}$
• B. $5x+4y=1$
• C. $5x+4y=0$
• D. $y+\dfrac{5x}{4}=\dfrac{-50}{3}$

Answer 1

Answer: (C)

$5x+4y=0$

Answer 2

Given that

$x+2y-10=0$……………………(1)

$2x+y+5=0$………………………(2)

Now, multiply $2$ in equation (1)

⇒$2x+4y-20=0$………………...(3)

By subtracting (1) from (3) we get ;

⇒3y-25=0

by solving this ,

$y=\dfrac{25}{3},$

putting this value in the place of $y$ in equation (1), we get;

$x=\dfrac{-20}{3}$

Hence, checking the options which satisfy the value of intersection point, is 5x+4y=0..( Ans**.)**