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3 years ago

5

Solving proportions

d="TexFormula1" title=" \frac{1\3}{5} = \frac{a}{20} " alt=" \frac{1\3}{5} = \frac{a}{20} " align="absmiddle" class="latex-formula">

1 answer:

Olegator [25]3 years ago

8 0

Answer:

a = 4/3

Step-by-step explanation:

1/3 a

----- = -----

5 20

Using cross products

1/3 * 20 = 5a

20/3 = 5a

Divide each side by 5

20/3 * 1/5 = 5a/5

4/3 = a

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Step-by-step explanation:

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The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
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