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

Question

Accepted Answer

Correct answer: A. (a) Given: 4 ax+2 ay+c=0…..(i) 5 bx+2 by+d=0…..(ii) Eqn. (i) b - (ii) a - abx+ bc- ad=0 ⇒x= bc- ad abPutting the value of x in eqn. (ii), we get 5b ( bc- ad ab )+2 by+d=0 ⇒y= 4 ad-5 bc2 ab Point of intersection is P ( bc- ad ab , 4 ad-5 bc2 ab ) ∵P is in fourth quadrant and equidistant from the two coordinate axes. ∴- 4 ad-5 bc2 ab= bc- ad ab ⇒-4 ad+5 bc=2 bc-2 ad ⇒3 bc=2 ab ⇒3 bc-2 ad=0

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

Solution

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