Question

Parabola y^2=4ax passes through( 2, -8) find iths latus rectum

Answer 1

Step-by-step explanation:

I think this question belong to class 12th

Answer 2

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

$\green{\tt{\therefore{Length\:of\:latus\:rectum=32\:units}}}$

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

$\green{ \underline \bold{given :}} \\ \tt{: \implies eqn \: of \: parabola \: ({y}^{2} =4 ax}) \\ \\ \tt{: \implies point \: on \: parabola = (2, - 8) } \\ \\ \red{ \underline \bold{to \: find :}} \\ \tt{: \implies length \: of \: latus \: rectum = ?}$

• According to given question :

$\tt {: \implies {y}^{2} = 4ax} \\ \\ \to \text{2,- 8 \: is \: on \: parabola \: so, \: the}\\ \text{Eqn \: satisfy \: this \: point} \\ \\ \tt{: \implies { (- 8)}^{2} = 4 \times a \times 2} \\ \\ \tt{: \implies 64 = 8a} \\ \\ \tt{: \implies a = \frac{ 64}{8} } \\ \\ \green{\tt{: \implies a = 8}} \\ \\ \green{ \tt{: \implies Eqn \: of \: parabola \: is \: \: {y}^{2} = 32x}} \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies Length \: of \: latus \: rectum = 4a} \\ \\ \tt{: \implies Length \: of \: latus \: rectum = 4 \times 8} \\ \\ \green{\tt{: \implies Length \: of \: latus \: rectum = 32 \: units}}$