The length of the transverse axis of the hype | vedclass

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(A) The given equation is $3x^2 - 4y^2 = 32$.Dividing both sides by $32$,we get $\frac{3x^2}{32} - \frac{4y^2}{32} = 1$,which simplifies to $\frac{x^2

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$\frac{8\sqrt{2}}{\sqrt{3}}$

Vedclass · Answer

(A) The given equation is $3x^2 - 4y^2 = 32$.Dividing both sides by $32$,we get $\frac{3x^2}{32} - \frac{4y^2}{32} = 1$,which simplifies to $\frac{x^2}{32/3} - \frac{y^2}{8} = 1$.This is in the standard form of a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,where $a^2 = \frac{32}{3}$.Thus,$a = \sqrt{\frac{32}{3}} = \frac{\sqrt{16 	imes 2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}}$.The length of the transverse axis is $2a$.Therefore,$2a = 2 	imes \frac{4\sqrt{2}}{\sqrt{3}} = \frac{8\sqrt{2}}{\sqrt{3}}$.

The length of the transverse axis of the hyperbola $3x^2 - 4y^2 = 32$ is

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