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3 years ago

The equation of a circle is shown below.

1 answer:

kondor19780726 [428]3 years ago

3 0

The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being "r". Therefore, the center is located at point (1, -3) and is located in the fourth quadrant, last option. Hope this answers the question.

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A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

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
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

7 0

3 years ago

PLEASE HELP ASAP what is the value of x? enter your answer in the box.

nika2105 [10]

Answer:

x=5

Step-by-step explanation:

We can use proportions to solve this problem. Put the side of the small triangle over the side of the large triangle.

9 15

------ = ----------

2x-1 3x

Using cross products

9*3x = 15(2x-1)

27x = 30x-15

Subtract 30x from each side

27x-30x = 30x-30x -15

-3x = -15

Divide by -3

-3x/-3 = -15x/-3

x = 5

6 0

3 years ago

Y = 10x + 6 sollve this by doing what

Vladimir79 [104]

Answer:

x = -3/5

Step-by-step explanation:

y = 10x + 6

0 (- 6) = 10x + 6 (- 6)

-6/10 = 10x/10

-6/10 = x

-3/5 = x

6 0

3 years ago

In considering the water quality in and around the U.S., the EPA analyzes critical chemical and physical states: oxygen, nutrien

Karolina [17]

Answer:

wastewater and fertilizer runoff

Step-by-step explanation:

Factors such as temperature, pH electrochemical (redox) potential, and the transparency of air and water can affect the chemical and physical characteristics of ecological systems. This are as a result of activities like climate change, water contamination, and changes in water runoff.

Wastewater and fertilizer runoff causes low amount of dissolved oxygen in water, which affect biological communities and cycling thereby resulting in chemical and physical states changes.

3 0

3 years ago

HELO URGENT WILL GIVE BRAINLIEST IF CORRECT

yanalaym [24]

Answer:
Circle

Explanation:

6 0

2 years ago

Read 2 more answers