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3 years ago

What is the standard form of the equation of a circle that has its center at (-2, -3) and passes through the point (-2, 0)?

Mathematics

1 answer:

juin [17]3 years ago

5 0

Answer:

(x - h)^2 + (y - k)^2 = 3^2

Step-by-step explanation:

The most general standard form here is

(x - h)^2 + (y - k)^2 = r^2. Since we know the center is at (-2, -3), we rewrite this equation as

(x + 2)^2 + (y + 3)^2 = r^2.

Note that the center (-2, -3) and the point (-2, 0) lie on the same vertical line, and that the vertical distance from the center to this point is 3. This is also the radius of the circle. Thus, the equation of this circle is:

(x - h)^2 + (y - k)^2 = 3^2

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The graph of F(x), shown below in pink, has the same shape as the graph of G(x) = x2, but it is flipped over the x-axis and shif

Tasya [4]

We are given

graph of f(x) is same as g(x)

so,

$f(x)=g(x)=x^2$

Firstly, it is flipped over x-axis

It means that it is reflected about x-axis

so, we can multiply y-value by -1

and we get

$f(x)=-x^2$

now, it is shifted down by 2 units

So, we can subtract y-value by 2

and we get

$f(x)=-x^2-2$

so, our new equation is

$f(x)=-x^2-2$ ................Answer

3 0

4 years ago

Read 2 more answers

The midpoint of AB is M(1, 3). If the coordinates of A are(4,1), what are the coordinates of B?

Oxana [17]

Answer:

B(-2,5)

Step-by-step explanation:

$\frac{x + 4}{2} = 1 \\ 2 \times \frac{x + 4}{2} = 1 \times 2 \\ x + 4 = 2 \\ x = 2 - 4 \\ x = - 2 \\ \frac{y + 1}{2} = 3 \\ 2 \times \frac{y + 1}{2} = 3 \times 2 \\ y + 1 = 6 \\ y = 6 - 1 \\ y = 5$

Hope that this is helpful.

Have a nice day.

6 0

3 years ago

How to find slope intercept form when slope equals 3 over 4 passing through 8, 2

IgorC [24]

Answer:

The slope intercept form would be y = 3/4x - 4

Step-by-step explanation:

To find the slope intercept form of this line, we start with using our given information in point-slope form. Then we solve for y.

y - y1 = m(x - x1)

y - 2 = 3/4(x - 8)

y - 2 = 3/4x - 6

y = 3/4x - 4

8 0

3 years ago

Can someone help me find x ?

ivolga24 [154]

Answer:

x = 15

Step-by-step explanation:

Apply the keg rule to find x. The keg rule is given as:

Hypotenuse / leg = leg / part of the hypotenuse directly under the leg

Hypotenuse = 25

Leg = x

Part of the hypotenuse directly under the leg = 25 - 16 = 9

Plug in the values

25/x = x/9

Cross multiply

x*x = 25*9

x² = 225

x = √225

x = 15

7 0

3 years ago

Add the mixed numbers.

klio [65]

9514 1404 393

Answer:

1 5/24 + 7 22/24 = 8 27/24

Step-by-step explanation:

No change is required to the fraction on the first line:

1 5/24 = 1 5/24

The fraction on the second line can be multiplied by 2/2 to make its denominator 24.

7 11/12 = 7 22/24

The fraction on the third line is the sum of the fractions on the other two lines. It is an improper fraction. We know this because the integer portion of the sum is shown as 8, not 9, as it would be if the fraction were reduced.

5/24 +22/24 = 27/24

Then the sum is ...

1 5/24 +7 22/24 = 8 27/24

_____

If the fraction on the final line were reduced, the sum would be 9 3/24 = 9 1/8.

7 0

3 years ago