Help Please!!!!!! The equation of a circle is x² + y² - 4x + 2y - 31 = 0. What is the center and the radius of the circle? Show your work.
Answers
The center of the circle is (2, - 1) and the radius is 6 units.
What are the types of equations of a circle?
The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.
The standard equation of a circle is x² + y² = r².
The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².
Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.
We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,
(- g, - f) and radius is .
Therefore, 2gx = - 4x and 2fy = 2y.
2g = - 4 and 2f = 2.
g = - 2 and f = 1.
- g = 2 and - f = - 1.
So, The center is (2, - 1).
And the radius is, .
= .
= .
= 6 units.
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Answer:
centre = (2, - 1), radius = 6
Step-by-step explanation:
Rearrange the equation by placing the x and y terms together and adding 31 to both sides
Given
x² + y² - 4x + 2y - 31 = 0, then
x² - 4x + y² + 2y = 31
Use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1
(x - 2)² + (y + 1)² = 36
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
compare to (x - 2)² + (y + 1)² = 36, then
centre = (2, - 1) and r = = 6
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But that's not in standard form (it's in slope-intercept form). So, to change the equation into standard form, add 15x to each side.
y = -15x + 90
y + 15x = -15x + 90 + 15x
15x + y = 90
Hope this helped :)
x = weeks
Ans: y = $90 - $15x
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Answer is provided in the image attached.
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A fraction means (the top number) divided by (the bottom number).
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is the decimal form of the fraction.
If you'll either pick up your pencil, or pick up your calculator, and divide 6 by 12 ,
you will get the decimal form of the fraction 6/12 . If you don't get 0.5 then you
made a mistake and you should try again.
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3 12
4 16
5 20
And the function graph above what is the input what is the output
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To then solve this you add 8 to both sides x/3=54
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