Question

For the parabola (y−2)2=2x+3
length of latus rectum is

Answer 1

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

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

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Eqn \: of \: parabola \: (y - 2)^{2} = 2x + 3 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length \: of \: latus \: rectum = ?$

• According to given question :

$\tt: \implies (y - 2)^{2} = 2x + 3 \\ \\ \tt: \implies (y - 2)^{2} = 2(x + \frac{3}{2}) \\ \\ \tt: \implies (y - 2)^{2} = 4 \times \frac{1}{2} (x + \frac{3}{2} )\\ \\ \text{So, \: it \: is \: in \: the \: form} \\ \tt: \implies Y^{2} = 4aX \\ \\ \bold{Where: } \\ \tt \circ \: a = \frac{1}{2} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies latus \: rectum = 4a \\ \\ \tt: \implies latus \: rectum =4 \times \frac{1}{2} \\ \\ \green{\tt: \implies latus \: rectum =2 \: unit}$

Answer 2

$\large \underline{ \pink{ \boxed{ \bf \green{Required \: Answer}}}}$