SATHEE: Straight Line and Pair of Straight Lines 1 Question 20

Straight Line and Pair of Straight Lines 1 Question 20

20. Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ lies in the fourth quadrant and is equidistant from the two axes, then

(2014 Main)

(a) $2 b c - 3 a d = 0$

(b) $2 b c + 3 a d = 0$

(d) $3 b c + 2 a d = 0$

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Solution:

Let coordinate of the intersection point in fourth quadrant be $(α, - α)$ .

Since, $(α, - α)$ lies on both lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ .

$\begin{aligned} ∴ 4 a α - 2 a α + c = 0 \Rightarrow α = \frac{- c}{2 a} \\ and 5 b α - 2 b α + d = 0 \Rightarrow α = \frac{- d}{3 b} \end{aligned}$

From Eqs. (i) and (ii), we get

$\begin{aligned} \frac{- c}{2 a} & = \frac{- d}{3 b} \Rightarrow 3 b c = 2 a d \\ \Rightarrow 2 a d - 3 b c & = 0 \end{aligned}$

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Straight Line and Pair of Straight Lines 1 Question 20

20. Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes, then

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20. Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ lies in the fourth quadrant and is equidistant from the two axes, then