Question

If parabola y=4ax passes through the point (3,4) find the value of a

Answer 1

a=1/3 is the correct value of a. Plz mark brainliest if it helps.

Answer 2

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

$\green{\tt{\therefore{Value\:of\:a=\frac{4}{3}}}}$

$\green{\tt{\therefore{Length\:of\:latus\:rectum=\frac{16}{3}\:units}}}$

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

$\green{ \underline \bold{Given :}} \\ \tt{: \implies Eqn \: of \:arabola \: ({y}^{2} =4 ax}) \\ \\ \tt{: \implies Point \: on \: parabola = (3,4) } \\ \\ \red{ \underline \bold{To \: Find :}} \\ \tt{:\implies Value\:of\:a=?} \\\\\ \tt{: \implies Length \: of \: latus \: rectum = ?}$

• According to given question :

$\tt {: \implies {y}^{2} = 4ax} \\ \\ \to \text{3, 4 \: is \: on \: parabola \: so, \: the}\\ \text{Eqn \: satisfy \: this \: point} \\ \\ \tt{: \implies { 4}^{2} = 4 \times a \times 3} \\ \\ \tt{: \implies 16 = 12a} \\ \\ \tt{: \implies a = \frac{ 16}{12} } \\ \\ \green{\tt{: \implies a =\frac{4}{3}}} \\ \\ \green{ \tt{: \implies Eqn \: of \: parabola \: is \: \: {y}^{2} = \frac{16}{3}x}} \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies Length \: of \: latus \: rectum = 4a} \\ \\ \tt{: \implies Length \: of \: latus \: rectum = 4 \times \frac{4}{3}} \\ \\ \green{\tt{: \implies Length \: of \: latus \: rectum = \frac{16}{3} \: units}}$