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3 years ago

A parabola can be drawn given a focus of (2,-3) and and a directrix of y=-1. Write the equation of the parabola in any form.

Mathematics

1 answer:

Tanzania [10]3 years ago

5 0

Answer:

(x - 2)^2 = -4 (y + 2)

Step-by-step explanation:

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In the diagram, GB = 2x + 3..

zaharov [31]

Answer-

$\boxed{\boxed{GB=15\ units}}$

Solution-

From the attachment,

AD = AE, so FA is a median.

BD = BF, so BE is a median.

CF = CE, so DC is a median.

And G is the centroid.

From the properties of centroid, we know that

The centroid divides each median in a ratio of 2:1

So,

$\Rightarrow FG:AG=2:1$

$\Rightarrow \dfrac{FG}{AG}=\dfrac{2}{1}$

$\Rightarrow FG=2\times AG$

$\Rightarrow 5x=2\times (x+9)$

$\Rightarrow 5x=2x+18$

$\Rightarrow 3x=18$

$\Rightarrow x=6$

So, GB will be $2(6)+3=15$ units

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A parabola can be drawn given a focus of (2,-3) and and a directrix of y=-1. Write the equation of the parabola in any form.​

A parabola can be drawn given a focus of (2,-3) and and a directrix of y=-1. Write the equation of the parabola in any form.