Q86 / 160 · TS EAMCET 2020 (10 Sep Shift 1) · Mathematics

The straight lines $x+3 y-9=0$, $4 x+5 y-1=0, p x+q y+10=0$ are concurrent, if the line $5 x+6 y+10=0$ passes through the point

  • Correct answer
    A
    $(q,-p)$
  • B
    $(q, p)$
  • C
    $(p,-q)$
  • D
    $(p, q)$

Solution

It is given that lines $x+3 y-9=0$, $4 x+5 y-1=0, p x+q y+10=0$ are concurrent $\therefore \quad\left|\begin{array}{lll}1 & 3 & -9 \\ 4 & 5 & -1 \\ p & q & 10\end{array}\right|=0$ $\begin{aligned} & \Rightarrow 50+q-3(40+p)-9(4 q-5 p)=0 \\ & \Rightarrow 50+q-120-3 p-36 q+45 p=0 \\ & \Rightarrow 42 p-35 q-70=0 \\ & \Rightarrow-6 p+5 q+10=0 \end{aligned}$ So, $5 x+6 y+10=0$ passes through $(q,-p)$.

Hence, the correct answer is option: 'A'.

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