The differential equation for all t...
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The differential equation for all the straight lines which are at a unit distance from the origin is (B)(y+ (B) - 1301181626) 130118116261 V- (A)(y-4d=--() ©(y- --

IIT/JEE
Maths
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309
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Equation of the line: ( y=a x+b ); Distance from the line to origin: ( d=frac{|b|}{sqrt{a^{2}+1}}=1 rightarrow b=pm sqrt{a^{2}+1} ) So ( y=a x pm sqrt{a^{2}+1} rightarrow frac{d y}{d x}=frac{d}{d x}(a x pm sqrt{a^{2}+1}) rightarrow y^{prime}=a ) and ( y=y^{prime} x pm sqrt{y^{prime 2}+1} rightarrowleft(y-x y^{prime}right)^{2}=y^{prime 2}+1 )
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