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Art [367]
3 years ago
7

what is the general form of the equation of a circle with its Center at -2 1 and passing through -4 one

Mathematics
2 answers:
nydimaria [60]3 years ago
4 0

Answer:

x² + y² + 4x - 2y + 1 = 0

Step-by-step explanation:

The equation of a circle is given by the general equation;

(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius.

In this case; the center is (-2,1)

We can get radius using the formula for magnitude; √((x2-x1)² + (y2-y1)²)

Radius = √((-4- (-2))² + (1-1)²)

             = 2

Therefore;

The equation of the circle will be;

(x+2)² + (y-1)² = 2²

(x+2)² + (y-1)² = 4

Expanding the equation;

x² + 4x + 4 + y² -2y + 1 = 4 subtracting 4 from both sides;

x² + 4x + y² - 2y + 4 + 1 -4 = 0

= x² + y² + 4x - 2y + 1 = 0

Doss [256]3 years ago
3 0

Answer:

\large\boxed{x^2+y^2+4x-2y+1=0}

Step-by-step explanation:

The standard form of an equation of a circle:

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

(h, k) - center

r - radius

The general form of an equation of a circle:

x^2+y^2+Dx+Ey+F=0

We have the center (-2, 1). Substitute to the equation in the standard form:

(x-(-2))^2+(y-1)^2=r^2\\\\(x+2)^2+(y-1)^2=r^2

Put thr coordinates of the point (-4, 1) to the equation and calculate a radius:

(-4+2)^2+(1-1)^2=r^2\\\\r^2=(-2)^2+0^2\\\\r^2=4

Therefore we have the equation:

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

Convert to the general form.

Use (a\pm b)^2=a^2\pm 2ab+b^2

(x+2)^2+(y-1)^2=4\\\\x^2+2(x)(2)+2^2+y^2-2(y)(1)+1^2=4\\\\x^2+4x+4+y^2-2y+1=4\qquad\text{subtract 4 from both sides}\\\\x^2+y^2+4x-2y+1=0

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enot [183]

Answer: The probability is 1/9.

Step-by-step explanation:

First, let's define the possible outcomes of each dice:

Red: Forward (4 times), Backward (2 times)

Green : {1, 1, 2, 2, 3, 4}

We want to find the probability of moving backward 2 spaces.

Then we need to find the probability of rolling a "backward" in the red dice, and a 2 in the green dice.

First, the probability of rolling a backward in the red dice is equal to the quotient between the number of outcomes that are "backward", and the total number of outcomes in the dice (there are 2 backwards and 6 outcomes in total), this is:

p1 = 2/6 = 1/3.

And the probability of rolling a 2 in the green dice is equal to the quotient between the number of outcomes with a 2, and the total number of outcomes. (The 2 appears two times, and there are 6 possible outcomes):

p2 = 2/6 = 1/3.

Now, the probability of both events happening at the same time is equal to the product of the individual probabilities, then the probability of moving backwards 2 spaces is:

P = p1*p2 = (1/3)*(1/3) = 1/9.

7 0
3 years ago
8n-12=6n+6 I need help figuring out this answer I been having some troble
Gennadij [26K]
Solve the equation with the following steps:
8n-12=6n+6
Subtract 6n from both sides
2n-12=6
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2n=18
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8 0
3 years ago
Write 107% as a decimal. Pls with solutions
otez555 [7]

Answer:

1.07

Step-by-step explanation:

1 To convert to a decimal, divide the percent number by 100.

<h3>107÷100=1.07</h3>

2 Therefore, the decimal form is 1.07

<h3>1.07</h3>

5 0
2 years ago
Read 2 more answers
What is the simplified form of the expression -2(-5x - 8)?
Deffense [45]

Answer: 10x+16

Step-by-step explanation:

Use the distributive property a(b+c)= ab+ac

so

-2(-5x-8) = (-2 * -5x) - (-2* -8)

=

10x-(-16)

=10x+16

Hope this helped!

3 0
3 years ago
The system of equations
cupoosta [38]

Answer:

z = -12

Step-by-step explanation:

The given system of equations is:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From (2): 2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

Comparing (5) and (6)

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

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

But from (1): xy = x + y

Using this in (7), we have

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8)

Using this in (4)

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5..........................................(9)

Using this in (8)

x = 5(12/5)/7 = 12/7 .......................(10)

Using (10) in (5)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

4 0
4 years ago
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