Question

The length of latus rectum of the parabola
4y² + 2x - 20y +17 = 0 is :​

Answer 1

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

$\green{\tt{\therefore{Latus\:rectum=0.5\:units}}}$

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

$\green {\underline \bold{Given : }} \\ \tt{: \implies 4{y}^{2} +2x- 20y + 17=0 \: \: \: (Eqn \: of \: parabola} \\ \\ \red {\underline \bold{To \: Find : }} \\ \tt{: \implies Length \: of \: latus \: rectum =?}$

• According to given question :

$\tt{: \implies 4{y}^{2}+2x -20y + 17=0} \\ \\ \tt{: \implies 4{y}^{2} - 20y+25 = -2x - 17+25} \\ \\\tt{: \implies (2y-5)^{2} = -2(x - 4)} \\ \\ \tt{: \implies 4(y - \frac{5}{2})^{2} = -2(x -4)} \\ \\ \tt{: \implies {(y - \frac{5}{2})}^{2} = -4\times\frac{1}{8} (x - 4)} \\ \\ \text{So, \: it \:is \: in \: the \: form \: of}\\ \tt{ : \implies Y^{2} = -4aX} \\ \\ \bold{where : } \\ \tt{\circ \: a = \frac{1}{8} } \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies Latus \: rectum = 4a }\\ \\ \tt{: \implies Latus \: rectum = 4 \times \frac{1}{8} }\\ \\ \green{\tt{: \implies Latus \: rectum = 0.5 \: units }}$