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Byju's Answer

Standard XII

Mathematics

Slope Intercept Form of a Line

Assertion :Th...

Question

Assertion :The equation of hyperbola whose asymptotes are the lines $3 x - 4 y + 7 = 0$ & $4 x + 3 y + 1 = 0$ & which passes through origin is $(3 x - 4 y + 7) (4 x + 3 y + 1) = 7$ . Reason: The equation of the pair of asymptotes & hyperbola differ by a constant only.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Combined equation of the asymptotes is given by , $(3 x - 4 y + 7) (4 x + 3 y + 1) = 0$
$∴$ Combined equation of the hyperbola is given by $(3 x - 4 y + 7) (4 x + 3 y + 1) + λ = 0$
(as reason is true) It passes through origin'
$∴ λ = - 7$
So equation of hyperbola is $(3 x - 4 y + 7) (4 x + 3 y + 1) = 7$
Hence, option 'A' is correct.

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Assertion :The equation of hyperbola whose asymptotes are the lines 3x−4y+7=0 & 4x+3y+1=0 & which passes through origin is (3x−4y+7)(4x+3y+1)=7. Reason: The equation of the pair of asymptotes & hyperbola differ by a constant only.

Assertion :The equation of hyperbola whose asymptotes are the lines $3 x - 4 y + 7 = 0$ & $4 x + 3 y + 1 = 0$ & which passes through origin is $(3 x - 4 y + 7) (4 x + 3 y + 1) = 7$ . Reason: The equation of the pair of asymptotes & hyperbola differ by a constant only.