The directrix of a parabola is $x + 8 = 0$ and its focus is at $(4, 3)$ . Then, the length of the latusrectum of the parabola is

5

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9

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10

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12

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24

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Solution

The correct option is E $24$
Equation of parabola is
$| x + 8 | = \sqrt{{(x - 4)}^{2} + {(y - 3)}^{2}}$
$\Rightarrow x^{2} + 64 + 16 x = x^{2} + 16 - 8 x + {(y - 3)}^{2}$
$\Rightarrow {(y - 3)}^{2} = 24 (x + 2)$

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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. $x^{2} = 16 y$

x = 2

1, 5

x + y + 2 = 0

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