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Ksju [112]
1 year ago
14

The diameter of Circle \(Q\) terminates on the circumference of the circle at \((3,0)\) and \((-4,0)\). Write the equation of th

e circle in standard form. Show all of your work for full credit.
Mathematics
1 answer:
Dahasolnce [82]1 year ago
8 0

The equation of the given circle in the standard form is given as <u>(x + 0.5)² + y² = 3.5²</u>.

In the question, we are given that the diameter of Circle \(Q\) terminates on the circumference of the circle at \((3,0)\) and \((-4,0)\).

We are asked to write the equation of the circle in standard form.

The equation of the circle in standard form is given as (x - h)² + (y - k)² = r, where (h, k) is the center of the circle, and r is the radius of the circle.

The center of the circle can be found using the midpoint formula, as the center is the midpoint of the diameter.

Thus, the center is at ( (3 + (-4))/2, (0 + 0)/2 ) = ( -1/2, 0 ).

The length of the diameter can be calculated using the distance formula.

Thus, the length of the diameter of the circle is √((-4 - 3)² + (0 - 0)²) = √((-7)²) = √49 = 7.

The radius is half the length of the diameter.

Thus, the radius, r = 7/2.

Now, we have the center (h, k) = (-1/2, 0), and the radius, r = 7/2.

Thus, the equation of the circle in the standard form, (x - h)² + (y - k)² = r can be shown as:

(x - (-1/2))² + (y - 0)² = (7/2)²,

or, (x + 0.5)² + y² = 3.5².

Thus, the equation of the given circle in the standard form is given as <u>(x + 0.5)² + y² = 3.5²</u>.

Learn more about the equation of the circle at

brainly.com/question/1559324

#SPJ4

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  y = -1

Step-by-step explanation:

Sides marked with the same marking are congruent, so we have two equations:

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5 0
3 years ago
Write the standard equation of the circle with the given Center and radius:
Kipish [7]

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Answer:

  B.  (x +4)² +(y +5)² = 64

Step-by-step explanation:

The equation for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Filling in your given values, you have ...

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Simplifying, you get ...

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_____

<em>Additional comment</em>

As you learn more different "standard form" equations, it may be helpful to keep a list, along with reminders of what the variables stand for and how the equation is used.

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Jennifer went to the post office for stamps. She bought the same number of 8-cent stamps and 10-cent stamps. She also bought as
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Write it out as a set of equation:
Let x be number of 8 cent stamps, y be 10 cent stamps, and z be 2 cent stamps.
x=y
z=x+y
8x+10y+2z=440
Lets first solve for x:
from x=y and z=2x(from first equation) the last equation is
8x+10x+4x=440
22x=440
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know that x=20, you also know that y=20 as well, since z=x+y, z=40.
So 20 8-cent stamps, 20 10-cent stamps, and 40 2-cent stamps.
5 0
3 years ago
Read 2 more answers
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