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Maths-

General

Easy

Question

The radius of the director circle of the hyperbola $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ , is

$a - b$
$\sqrt{a - b}$
$\sqrt{a^{2} - b^{2}}$
$\sqrt{a^{2} + b^{2}}$

The correct answer is: $square root of a to the power of 2 end exponent minus b to the power of 2 end exponent end root$

Equation of director-circle of the hyperbola
$fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ is $x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent minus b to the power of 2 end exponent$
So, radius $equals square root of a to the power of 2 end exponent minus b to the power of 2 end exponent end root$ .

Related Questions to study

A black colored compound (A)on reaction with diluteH₂SO₄ gives a gas(B) which on passing in a solution ofan acid (C) gives a white turbidity (D). Gas (B) when placed in an acidified solution of acompound (E)gives aprecipitate(F)solubleindiluteHNO₃.Afterboilingthissolution,whenanexcessofNH₄OHisadded,bluecoloredcompound(G)is formed. Tothissolution on additionofCH₃COOHandaqueous K₄[Fe(CN)₆],a chocolate precipitate(H)is obtained. On addition of an aqueous solution ofBaCl₂ to an aqueous solutionofE,awhitepptinsolubleinHNO₃isobtained. Identify H:

A black colored compound (A)on reaction with diluteH₂SO₄ gives a gas(B) which on passing in a solution ofan acid (C) gives a white turbidity (D). Gas (B) when placed in an acidified solution of acompound (E)gives aprecipitate(F)solubleindiluteHNO₃.Afterboilingthissolution,whenanexcessofNH₄OHisadded,bluecoloredcompound(G)is formed. Tothissolution on additionofCH₃COOHandaqueous K₄[Fe(CN)₆],a chocolate precipitate(H)is obtained. On addition of an aqueous solution ofBaCl₂ to an aqueous solutionofE,awhitepptinsolubleinHNO₃isobtained. Identify H:

Chemistry-General

A black colored compound (A)on reaction with diluteH₂SO₄ gives a gas(B) which on passing in a solution ofan acid (C) gives a white turbidity (D). Gas (B) when placed nan acidified solution of a compound(E)gives a precipitate(F)solubleindiluteHNO₃.Afterboilingthissolution,whenanexcessofNH₄OHisadded,bluecoloredcompound(G) is formed. To this solution on additionofCH₃COOHandaqueous K₄[Fe(CN)₆],a chocolate precipitate(H)isobtained. On addition of an aqueous solution ofBaCl₂ to an aqueous solutionofE,awhitepptinsolubleinHNO₃isobtained. Identify C:

A black colored compound (A)on reaction with diluteH₂SO₄ gives a gas(B) which on passing in a solution ofan acid (C) gives a white turbidity (D). Gas (B) when placed nan acidified solution of a compound(E)gives a precipitate(F)solubleindiluteHNO₃.Afterboilingthissolution,whenanexcessofNH₄OHisadded,bluecoloredcompound(G) is formed. To this solution on additionofCH₃COOHandaqueous K₄[Fe(CN)₆],a chocolate precipitate(H)isobtained. On addition of an aqueous solution ofBaCl₂ to an aqueous solutionofE,awhitepptinsolubleinHNO₃isobtained. Identify C:

Chemistry-General

A black colored compound(A)on reaction with dil. H₂SO₄ gives a gas(B)which onpassingin a solution of anacid (C) gives a white turbidity (D). Gas (B)when passed in an acidified solution of a compound(E) gives a black precipitate (F) which is soluble in hot concentrated (C).After boiling this solution whene xcess of ammonia solution is added, a blue colored compound (G) is formed. To the solution of(E), onaddition of acetic acid and aqueous potassium ferrocyanide, a chocolate brown precipitate (H) is formed.OnadditionofanaqueoussolutionofBaCl₂toan aqueoussolutionof(E),white precipitate insoluble in HNO₃isobtained. To which of the following property, will the compound(E)respond?

A black colored compound(A)on reaction with dil. H₂SO₄ gives a gas(B)which onpassingin a solution of anacid (C) gives a white turbidity (D). Gas (B)when passed in an acidified solution of a compound(E) gives a black precipitate (F) which is soluble in hot concentrated (C).After boiling this solution whene xcess of ammonia solution is added, a blue colored compound (G) is formed. To the solution of(E), onaddition of acetic acid and aqueous potassium ferrocyanide, a chocolate brown precipitate (H) is formed.OnadditionofanaqueoussolutionofBaCl₂toan aqueoussolutionof(E),white precipitate insoluble in HNO₃isobtained. To which of the following property, will the compound(E)respond?

Chemistry-General

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