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Anestetic [448]
3 years ago
12

A circle in the xy-plane has a diameter with endpoints whose coordinates are negative 1 comma negative 3 and 7 comma 3. if the p

oint with coordinates 0 comma b lies on the circle and b is greater than 0, what is the value of b ?
Mathematics
2 answers:
DerKrebs [107]3 years ago
8 0

<span>First we look for the coordinates of the center of the circle. For this, we use the following formula:</span>

<span> ((x1 + x2) / 2, (y1 + y2) / 2)</span>

<span> Where,</span>

<span> (x1, y1) = (- 1, -3)</span>

<span> (x2, y2) = (7, 3)</span>

<span> Substituting values we have:</span>

<span> ((-1 + 7) / 2, (-3 + 3) / 2)</span>

<span> ((6) / 2, (0) / 2)</span>

<span> (3, 0)</span>

<span> We are now looking for the diameter of the circle. For this we use the formula of distance between points:</span>

<span> d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)</span>

<span> Substituting values:</span>

<span> d = root ((7 - (- 1)) ^ 2 + (3 - (- 3)) ^ 2)</span>

<span> d = 10</span>

<span> Then, the radius of the circle is:</span>

<span> r = d / 2 = 10/2</span>

<span> r = 5</span>

<span> The circle equation will be</span>

<span> (x-h) ^ 2 + (y-k) ^ 2 = r ^ 2</span>

<span> Where,</span>

<span> (h, k) = (3, 0)</span>

<span> r = 5</span>

<span> Substituting</span>

<span> (x-3) ^ 2 + (y-0) ^ 2 = 5 ^ 2</span>

<span><span> Substituting</span></span>

<span><span> (x, y) = (0, b)</span></span>

<span><span> (0-3) ^ 2 + (b-0) ^ 2 = 5 ^ 2</span></span>

<span><span> b = root (25-9)</span></span>

<span><span> b = root (16)</span></span>

<span><span> b = 4</span></span>

<span><span> Answer</span></span>

<span><span> the value of b is</span></span>

<span><span> <span>b = 4</span></span></span>


In-s [12.5K]3 years ago
5 0

Answer:

b = 4

Step-by-step explanation:

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schepotkina [342]

Answer: A: (x + 4)² + (y - 5)² = 8

<u>Step-by-step explanation:</u>

The equation of a circle is: (x - h)² + (y - k)² = r²     where

  • (h, k) is the center of the circle
  • r is the radius of the circle

To find the equation of circle A, we need (h, k) and r².

It is given that (h, k) = (-4, 5)

The distance between the center of circles A and B is the radius of circle A.

Let's find the center of circle B by completing the square:

x² - 4x + ____ +  y² + 6y + _____ = 12 + ____ + _____

     ↓                            ↓      

  h = -4/2                    k = 6/2

  h = -2                       k = 3              →  Circle B has center (-2, 3)

Now let's find the distance between the center of circles A and B:

(r_A)^2=d^2=(x_A-x_B)^2+(y_A-y_B)^2

                = (-4 - (-2))² + (5 - 3)²

                =     (-2)²     +     2²

                =       4        +     4

                = 8

Now we have the the center (h, k) and the r² for circle A:

(h, k) = (-4, 5) and r² = 8   →    (x + 4)² + (y - 5)² = 8

 

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3 years ago
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