Equation of the directrix of the parabola $y^{2} = 5 x - 4 y - 9$ is

2 x + 1 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 x + 1 = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6 x + 1 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 x - 1 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $4 x + 1 = 0$
Given $y^{2} = 5 x - 4 y - 9$
$\Rightarrow y^{2} + 4 y + 4 = 5 (x - 1)$
$\Rightarrow (y + 4)^{2} = 5 (x - 1)$
$4 a = 5 \Rightarrow a = \frac{5}{4}$
For a parabola $(y - k)^{2} = 4 a (x - h),$ equation of directrix is $x = h - a$
Equation of directrix is $x = 1 - \frac{5}{4} = - \frac{1}{4}$
Directrix of given parabola is $4 x + 1 = 0$

Suggest Corrections

Similar questions

y^{2} + 4 y + 4 x + 2 = 0

x^{2} + y^{2} + 6 x + 4 y + 4 = 0

x^{2} + y^{2} - 2 x = 0

y - 1 = 0

4 x - 3 y - 9 = 0

x^{2} + y^{2} - 4 x - 10 y + 28 = 0

x^{2} + y^{2} + 4 x - 6 y + 4 = 0

x - 1 = 0, 3 x + 4 y - 21 = 0

\sqrt{2}

y^{2} + 4 y + 4 x + 2 = 0

y^{2} + 4 y + 4 x + 2 = 0

Join BYJU'S Learning Program