The equation of a parabola is given by $x^{2} - 8 x - 4 y + 32 = 0$ . Then

focus is

(4, 4)

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axis is

x = 4

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directrix is

y = 3

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vertex is

(4, 4)

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Solution

The correct options are
A directrix is $y = 3$
B axis is $x = 4$
D vertex is $(4, 4)$
$x^{2} - 8 x - 4 y + 32 = 0$
$(x - 4)^{2} - 4 y + 16 = 0$
$(x - 4)^{2} = 4 (y - 4)$
Comparing with $x^{2} = 4 a y$
Axis is $x - 4 = 0 \Rightarrow x = 4$
$a = 1$
Vertex is $(4, 4)$
$y = - a$ is equation of directrix
$\Rightarrow y - 4 = - 1 \Rightarrow y = 3$ is equation of directrix.

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Similar questions

List-l	List - II
A. Length of the latusrectum of the parabola $3 y^{2} = - 4 x$	1. $(5, 2)$
B.Equation of the parabola whose focus $($ 0,4 $)$ and directrix $x + 4 = 0$ is	2. $\frac{- 4}{3}$
C. The focus of the parabola $(y - 2)^{2} = 8 (x - 3)$ is	3. $\frac{4}{3}$
D. Equation of the parabola whose vertex $(- 1, - 2)$ latusrectum 4 and axis is parallel to y-axis	4. $(x + 1)^{2} = 4 (y + 2)$
	5. $x^{2} = 16 y$