Lines are drawn parallel to the line 4x−3y+2=0, at a distance 35 units from the origin. Then which of the following points lies on any of these lines ?
A
(14,13)
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B
(14,−13)
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C
(−14,−23)
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D
(−14,23)
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Solution
The correct option is D(−14,23) Equation of line parallel to the line 4x−3y+2=0 is 4x−3y+λ=0...(1) Distance of line from the origin is ∣∣
∣
∣∣4(0)−3(0)+λ√42+(−3)3∣∣
∣
∣∣=35 ⇒λ=±3 putting the value of λ in equation (1) ∴ the required lines are 4x−3y+3=0 and 4x−3y−3=0 Point (−14,23) satisfies the line 4x−3y+3=0