Question

The least positive value $t$ so that the lines $x=2t,y-16=0$ and $y=2tx$ are concurrent is

• A. $2$
• B. $4$
• C. $16$
• D. $8$

Answer 1

The correct option is A $2$

If more than two lines passing through the same point then the lines are called concurrent lines.

Given lines are,

$x=2t,$ $\dots \left(1\right)$

$y-16=0$ $\dots \left(2\right)$

$y=2tx$ $\dots \left(3\right)$

substitute $\left(3\right)$ in $\left(2\right)$

$⟹16=2tx$

now substitute $x$ from $\left(1\right)$

$⟹16=2t\left(2t\right)=4t^2$

$⟹t^2=4=2$