8. Find the eqation of the straight line passing through the point of interscetion of the line x+y+9=0 and 3x-2y+2=0 and is perpendicular to the line 4x+5y+1=0
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Step-by-step explanation:
Given lines are x+y+9=0 and 3x-2y+2=0
To find the point of contact, multiply the first equation by 3 and subtract from the second equation i.e.,
(3x+3y+27)-(3x-2y+2)=0
⇒ 5y+25=0
⇒ y= -5
Putting y = -5 in the first equation, we get,
x = -4
So, the required line is passing through (-4,-5)
It is also given that the required line is perpendicular to the line 4x+5y+1=0
⇒5y = -4x-1
So, slope of required line ,
Now, equation of line ≡
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