The directrix of the parabola x2-4 x-8 y-12-0 isA- x-1B- y -1C- y-0D- x-1

The correct option is B y= 1 Given : x^2 4x 8y+12=0 ⇒ (x 2)^2 4 8y+12=0 ⇒ (x 2)^2=8y 8 ⇒ (x 2)^2=8(y 1) Putting X=x 2,Y=y 1 : X^2=8Y Comparing with X^2=4aY: ...

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Standard XII

Mathematics

Directrix

The directrix...

Question

The directrix of the parabola $x^{2} - 4 x - 8 y + 12 = 0$ is

y=0

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x=1

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y=-1

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x=-1

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Solution

The correct option is C
y=-1

Given : $x^{2} - 4 x - 8 y + 12 = 0$

$\Rightarrow (x - 2)^{2} - 4 - 8 y + 12 = 0$

$\Rightarrow (x - 2)^{2} = 8 y - 8$

$\Rightarrow (x - 2)^{2} = 8 (y - 1)$

Putting X=x-2,Y=y-1 :

$X^{2} = 8 Y$

Comparing with $X^{2} = 4 a Y :$

a=2

Equation of the directrix :

Y=-a

$\Rightarrow Y = - 2$

$\Rightarrow y - 1 = - 2$

$\Rightarrow y = - 2 + 1$

$\Rightarrow y = - 1$

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Similar questions

Q. The directrix of the parabola x² − 4x − 8y + 12 = 0 is
(a) y = 0
(b) x = 1
(c) y = − 1
(d) x = − 1

Q. The mirror image of the directrix of the parabola

y = x^{2} + 5 x + 7

in the line mirror

x + y = 1

Q. The directrix of the parabola

x^{2} - 4 x - 8 y + 12 = 0

is:

Q. The equation of the parabola with focus (0, 0) and directrix x + y = 4 is
(a) x² + y² − 2xy + 8x + 8y − 16 = 0
(b) x² + y² − 2xy + 8x + 8y = 0
(c) x² + y² + 8x + 8y − 16 = 0
(d) x² − y² + 8x + 8y − 16 = 0

Q. If

\frac{x}{y} + \frac{y}{x} = - 1

, where x ≠ 0 and y ≠ 0, then the value of (x³ − y³) is
(a) 1
(b) −1
(c) 0
(d)

\frac{1}{2}

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The directrix of the parabola x2−4x−8y+12=0 is

The correct option is C y=-1 Given : x2−4x−8y+12=0 ⇒ (x−2)2−4−8y+12=0 ⇒ (x−2)2=8y−8 ⇒ (x−2)2=8(y−1) Putting X=x-2,Y=y-1 : X2=8Y Comparing with X2=4aY: a=2 Equation of the directrix : Y=-a ⇒ Y=−2 ⇒ y−1=−2 ⇒ y=−2+1 ⇒ y=−1

The directrix of the parabola $x^{2} - 4 x - 8 y + 12 = 0$ is