Question

Find length of latus rectum of a parabola y sqaure = 4ax passing through the point (2,-6)

Answer 1

length of latus rectum of a parabola = 4a,

where a is focal length .

equation of parabola

⇒ y² =4ax

and the parabola passes through (2,-6)

putting these value in equation of parabola

        (-6)*(-6)=4a*2

           36=8a

           a=36/8

⇒length of latus rectum = 4*(36/8)

                                          =18 units

Answer 2

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

$\green{\tt{\therefore{Length\:of\:latus\:rectum=18\:units}}}$

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

$\green{ \underline \bold{Given :}} \\ \tt{: \implies Eqn \: of \:arabola \: ({y}^{2} =4 ax}) \\ \\ \tt{: \implies Point \: on \: parabola = (2,-6) } \\ \\ \red{ \underline \bold{To \: Find :}} \\ \tt{: \implies Length \: of \: latus \: rectum = ?}$

• According to given question :

$\tt {: \implies {y}^{2} = 4ax} \\ \\ \to \text{2, -6 \: is \: on \: parabola \: so, \: the}\\ \text{Eqn \: satisfy \: this \: point} \\ \\ \tt{: \implies {-6}^{2} = 4 \times a \times 2} \\ \\ \tt{: \implies 36 = 8a} \\ \\ \tt{: \implies a = \frac{36}{8} } \\ \\ \green{\tt{: \implies a =\frac{9}{2}}} \\ \\ \green{ \tt{: \implies Eqn \: of \: parabola \: is \: \: {y}^{2} = 18x}} \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies Length \: of \: latus \: rectum = 4a} \\ \\ \tt{: \implies Length \: of \: latus \: rectum = 4 \times \frac{9}{2}} \\ \\ \green{\tt{: \implies Length \: of \: latus \: rectum = 18\: units}}$