Question

Length of latus rectum of hyperbola x^2/4 - y^2/9 is?
Plz help me

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Length\:of\:latus\:rectum=\frac{3}{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Eqn \: of \: hyperbola \: \frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{9} = 1 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length \: of \: latus \: rectum = ?$

• According to given question :

$\tt: \implies \frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{9} = 1 \\ \\ \tt: \implies \frac{ {x}^{2} }{ {2}^{2} } - \frac{ {y}^{2} }{ {3}^{2} } = 1 \\ \\ \text{So, \: it \: is \: in \: the \: form \: of} \\ \tt: \implies \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1 \\ \\ \bold{Where: } \\ \tt\circ \: a = 2 \\ \\ \tt \circ \: b = 3 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Length \: of \: latus \: rectum = \frac{2b}{ {a}^{2} } \\ \\ \tt: \implies Length \: of \: latus \: rectum = \frac{2 \times 3}{4} \\ \\ \green{\tt: \implies Length \: of \: latus \: rectum = \frac{3}{2} }$

Answer 2

$\huge{\underline{\underline{\mathtt{\red{Answer}}}}}$

$\frac{3}{2}$

$\huge{\underline{\underline{\mathtt{\red{Solution}}}}}$

${ \boxed{ \boxed{latus \: rectum \: = \frac{2b}{ {a}^{2} } }}}$

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Equation of Hyperbola = x²/4 - y²/9 = 1

We know that the standard form of hyperbola equation is

⇝ x²/a² - y²/b²

Or another form is

⇝ y²/a² - x² / b²

It means that the given equation is already in its standard form .

So comparing it with its standard form , we get .

⇝ a² = 4 → a = 2

⇝ b² = 9 → b = 3

Formula of latus rectum is mentioned above .

$\red {\implies \: \frac{2b}{ {a}^{2} } }$

$\red{ \implies \: \frac{2 \times 3}{4} }$

${ \boxed{ \mathtt{ \purple{latus \: rectum \: \implies \: \frac{3}{2} }}}}$

So our answer is 3/2 .

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Related points :-

☆ Eccentricity ( e ) = c/a

☆ A hyperbola in which a = b is called

equilateral hyperbola.