Equation of directrix of the parabola y^2=5x-4y-9

1.	Equation of directrix of the parabola y^2=5x-4y-9
Answer» $\blue{\bold{\underline{\underline{Answer:}}}}$ $\green{\tt{\therefore{x+\frac{1}{4}=0}}}\\$ $\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$ $\green{\underline \bold{<klux>GIVEN</klux>:}} \\ \tt: \implies {y}^{2} = 5x - 4y - 9 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Eqn \: of \: directrix = ?$ • ACCORDING to given QUESTION : $\tt: \implies {y}^{2} = 5x - 4y - 9 \\ \\ \tt: \implies {y}^{2} + 4y = 5x - 9 \\ \\ \tt: \implies {y}^{2} + 4y + 4 = 5x - 9 + 4 \\ \\ \tt: \implies {(y - 2)}^{2} = 5x - 5 \\ \\ \tt: \implies {(y - 2)}^{2} = 5(x - 1) \\ \\\tt: \implies {(y - 2)}^{2} = 4 \times \frac{5}{4}(x - 1) \\ \\ \text{So, \: it \: is \: in \: the \: form \: of}\\ \\ \tt: \implies Y^{2} = 4aX \\ \\ \bold{Where : } \\ \tt \circ \: a = \frac{5}{4} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Eqn \: of \: directrix \to X = - a \\ \\ \tt: \implies Eqn \: of \: directrix \to x - 1 = - \frac{5}{4} \\ \\ \tt: \implies Eqn \: of \: directrix \to x = - \frac{5}{4} + 1 \\ \\ \tt: \implies Eqn \: of \: directrix \to x = \frac{ - 1}{4} \\ \\ \green{\tt: \implies Eqn \: of \: directrix \to x + \frac{1}{4} = 0}$

Answer»

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

$\green{\tt{\therefore{x+\frac{1}{4}=0}}}\\$

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

$\green{\underline \bold{<klux>GIVEN</klux>:}} \\ \tt: \implies {y}^{2} = 5x - 4y - 9 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Eqn \: of \: directrix = ?$

• ACCORDING to given QUESTION :

$\tt: \implies {y}^{2} = 5x - 4y - 9 \\ \\ \tt: \implies {y}^{2} + 4y = 5x - 9 \\ \\ \tt: \implies {y}^{2} + 4y + 4 = 5x - 9 + 4 \\ \\ \tt: \implies {(y - 2)}^{2} = 5x - 5 \\ \\ \tt: \implies {(y - 2)}^{2} = 5(x - 1) \\ \\\tt: \implies {(y - 2)}^{2} = 4 \times \frac{5}{4}(x - 1) \\ \\ \text{So, \: it \: is \: in \: the \: form \: of}\\ \\ \tt: \implies Y^{2} = 4aX \\ \\ \bold{Where : } \\ \tt \circ \: a = \frac{5}{4} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Eqn \: of \: directrix \to X = - a \\ \\ \tt: \implies Eqn \: of \: directrix \to x - 1 = - \frac{5}{4} \\ \\ \tt: \implies Eqn \: of \: directrix \to x = - \frac{5}{4} + 1 \\ \\ \tt: \implies Eqn \: of \: directrix \to x = \frac{ - 1}{4} \\ \\ \green{\tt: \implies Eqn \: of \: directrix \to x + \frac{1}{4} = 0}$

Equation of directrix of the parabola y^2=5x-4y-9

• ACCORDING to given QUESTION :

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