The length of transverse axis of the parabola | vedclass

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Question

(a) The given equation may be written as $\frac{{{x^2}}}{{32/2}} - \frac{{{y^2}}}{8} = 1$ or $\frac{{{x^2}}}{{{{\left( {4\sqrt 2 /\sqrt 3 } \right)}^2

Vedclass · Accepted Answer

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

Vedclass · Answer

(a) The given equation may be written as $\frac{{{x^2}}}{{32/2}} - \frac{{{y^2}}}{8} = 1$ or $\frac{{{x^2}}}{{{{\left( {4\sqrt 2 /\sqrt 3 } ight)}^2}}} - \frac{{{y^2}}}{{{{(2\sqrt 2 )}^2}}} = 1$.

Comparing the given equation with $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$,

we get ${a^2} = {\left( {\frac{{4\sqrt 2 }}{{\sqrt 3 }}} ight)^2}$ or $a = \frac{{4\sqrt 2 }}{{\sqrt 3 }}.$

Therefore length of transverse axis of a hyperbola

$ = 2a = 2 	imes \frac{{4\sqrt 2 }}{{\sqrt 3 }} = \frac{{8\sqrt 2 }}{{\sqrt 3 }}.$

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

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