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Sequences And Series

Question
CBSEENMA11015474
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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

  • 2bc-3ad =0 

  • 2bc+3ad =0

  • 2ad-3bc =0

  • 3bc+2ad=0

Solution

C.

2ad-3bc =0

Let coordinate of the intersection point in the fourth quadrant be (α, -α) lies on both lines 4ax +2ay +c =0 and 5bx +2by +d =0
therefore space 4 aα space minus 2 aα space plus straight c space equals 0 space rightwards double arrow straight alpha space equals space fraction numerator negative straight c over denominator 2 straight a end fraction space.... space left parenthesis straight i right parenthesis 5 bα space minus 2 bα space plus straight d space equals 0 space rightwards double arrow space straight alpha space equals space fraction numerator negative straight d over denominator 3 straight b end fraction space..... space left parenthesis ii right parenthesis From space Eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get fraction numerator negative straight c over denominator 2 straight a end fraction space equals space fraction numerator negative straight d over denominator 3 straight b end fraction rightwards double arrow space 3 bc space equals space 2 ad rightwards double arrow 2 ad minus 3 bc space equals space 0

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