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inn [45]
3 years ago
10

Find the coordinates of the focus and equation of the directrix for the parabola given by

Mathematics
2 answers:
Romashka [77]3 years ago
5 0

Answer:

The answers to your three problem question are shown

1) the value of p is

p = -1

2) The coordinates of the focus are

Focus =  (-1,0)

3) The equation of the directrix is

Directrix

x = 1

Step-by-step explanation:

The general equation for this parabola is

y^2 = 4px

Problem 1

Find the value of p.

We are told that the equation of the problem is

y^2 = -4x

And the general formula is

y^2 = 4px

From there, we can deduce that

p = -1, because

y^2 = 4(-1)x = -4x

This means that p = -1

Problem 2

Find the focus

To find the focus we can see the equations attached below for the focus, vertex and directrix.

In these case, the equations still apply, even though the variable is inverted, we just need to adjust it

y^2 = -4x =>

x = (-1/4)*y^2

x = a*y^2 + b*y +c

Focus

((4ac -b^2  + 1)/4a, -b/2a)

But, b = 0 and c = 0

=>

(1/4a,0) = (1/4(-1/4),0) = (-1,0)

Focus =  (-1,0)

Problem 3

Find the directrix

The equation is

x = c - (b^2 + 1).4a

But, b = 0 and c = 0

x = -4*a

x = -4* (-1/4) = 1

x = 1

Directrix

x = 1

sukhopar [10]3 years ago
4 0

Answer: P is -1

Focus is (-1,0)

Directrix is X= 1

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Paolo Portraits charges $15 per photo with no sitting fee. The graph shows the fees for clear image studio.Compare the functions
liubo4ka [24]

Answer:

The rate of change of Paolo Portraits is $15 per photo and the rate of change of clear image studio is $12 per photo. Paolo Portraits charges are higher than the clear image studio.

Step-by-step explanation:

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