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lions [1.4K]
3 years ago
7

If the center of a circle is at (3,-6) and the diameter is 10 units, what is the equation for the circle

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
6 0

Answer:(x-3)^2+(y+6)^2=25

Step-by-step explanation:

Center Of The circle is at (3,-6)

Diameter=10

Radius(r)=10/2

Radius(r)=5

a=3

b=-6

Equation of circle=(x-a)^2+(y-b)^2=r^2

Equation of circle=(x-3)^2+(y-(-6))^2=5^2

Equation of circle=(x-3)^2+(y+6)^2=25

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Simplifying
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Reorder the terms:
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Solving
-3 + -7x + 5x2 = 8

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Factor a perfect square on the left side:
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Calculate the square root of the right side: 1.640121947

Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.

Subproblem 1
x + -0.7 = 1.640121947

Simplifying
x + -0.7 = 1.640121947

Reorder the terms:
-0.7 + x = 1.640121947

Solving
-0.7 + x = 1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

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-0.7 + 0.7 + x = 1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
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Simplifying
x = 2.340121947

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Simplifying
x + -0.7 = -1.640121947

Reorder the terms:
-0.7 + x = -1.640121947

Solving
-0.7 + x = -1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
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x = -1.640121947 + 0.7

Combine like terms: -1.640121947 + 0.7 = -0.940121947
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Simplifying
x = -0.940121947

Solution
The solution to the problem is based on the solutions
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x = {2.340121947, -0.940121947}
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