Question

the latus rectum of the parabola y^2=5x+4y+1 is?

Answer 1

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Answer 2

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

$\green{\tt{\therefore{Latus\:rectum=5\:units}}}$

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

$\green {\underline \bold{Given : }} \\ \tt{: \implies {y}^{2} = 5x + 4y + 1 \: \: \: (Eqn \: of \: parabola} \\ \\ \red {\underline \bold{To \: Find : }} \\ \tt{: \implies Length \: of \: latus \: rectum =?}$

• According to given question :

$\tt{: \implies {y}^{2} = 5x + 4y + 1} \\ \\ \tt{: \implies {y}^{2} - 4y = 5x + 1} \\ \\\tt{: \implies {y}^{2} - 4y + 4 - 4 = 5x + 1} \\ \\ \tt{: \implies (y - 2 )^{2} = 5x + 5} \\ \\ \tt{: \implies {(y - 2)}^{2} = 4 \times \frac{5}{4} (x + 1)} \\ \\ \text{So, \: it \:is \: in \: the \: form \: of}\\ \tt{ : \implies Y^{2} = 4aX} \\ \\ \bold{where : } \\ \tt{\circ \: a = \frac{5}{4} } \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies Latus \: rectum = 4a }\\ \\ \tt{: \implies Latus \: rectum = 4 \times \frac{5}{4} }\\ \\ \green{\tt{: \implies Latus \: rectum = 5 \: units }}$