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प्रश्न
Find the equation of a line passing through the intersection of `"x"/10 + "y"/5` = 14 and `"x"/8 + "y"/6` = 15 and perpendicular to the line x - 2y = 5
उत्तर
`"x"/10 + "y"/5` = 14 ⇒ x + 2y = 140......(1)
`"x"/8 + "y"/6` = 15 ⇒ 3x + 4y = 360........(2)
(1) can be rewritten as 2x + 4y = 280......(3)
(2) can be rewritten as 3x _ 4y = 360........(4)
subtracting (3) from (4), we get
x = 80
y = 30
Point of intersection of (1) and (2) is (80,30)
slope of x - 2y = 5 is`1/2`
Equation of required line is `("y" - "y"_1)/("x" - "x"_1)` = m
`("y" - 30)/("x" -80)` = -2
⇒ -2x + 160 = y - 30
⇒ 2x + y = 190
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