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BigorU [14]
3 years ago
15

Which is the standard equation of a circle with diameter with A(0, -1) and B(2, 1)?

Mathematics
1 answer:
Ann [662]3 years ago
8 0

The standart equation:

(x - xc)² + (y - yc)² = r²

For this case, we have the diameter given by 2 points, A and B, the center will be the middle point of this line. We can get the middle point of this line adding both x's and dividing by two, the same for y.

M = (0+2/2, -1+1/2)

M = (2/2, 0/2)

M = (1, 0)

For the radius we need to know the distance between the middle point and A or B,

d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

Let's use B.

d = \sqrt{(1-2)^2+(0-1)^2}

d=\sqrt{(-1)^2+(-1)^2}

d=\sqrt{1+1}

d=\sqrt{2}

Knowing the radius we can put all in the formule

(x - xc)² + (y - yc)² = r²

(x - 1)² + (y - 0)² = \sqrt{2}^2

(x - 1)² + y² = 2

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Answer:

The Length of swimming pool is 8.35 feet

The width of swimming pool is 5.35 feet

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Given as :

The length of swimming pool is 3 feet longer that its width

Let The width of swimming pool = w  feet

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The width of deck = w' = w + 2 + 2 = (w + 4) feet

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So, L' = (w + 3 + 4) feet

I.e L' = (w + 7) feet

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Or, w² + 11 w - 88 = 0

Solving the quadratic equation as

ax² + bx + c = 0

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Hence, The Length of swimming pool is 8.35 feet

And The width of swimming pool is 5.35 feet

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