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Find the equation of the circle that has the center (2,0) and passes through (-1,-5)

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Answer to a math question Find the equation of the circle that has the center (2,0) and passes through (-1,-5)

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Sigrid

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116 Answers

Solution:
1. Given:
- Center of the circle:

(2, 0)

- Point on the circle:

(-1, -5)

2. Use the standard equation of a circle:
-

(x - h)^2 + (y - k)^2 = r^2

where

(h, k)

is the center and

is the radius.

3. Substitute the center into the equation:
-

(x - 2)^2 + (y - 0)^2 = r^2

- Simplifies to:

(x - 2)^2 + y^2 = r^2

4. Substitute point

(-1, -5)

to find

r^2

:
-

((-1) - 2)^2 + ((-5) - 0)^2 = r^2

(-3)^2 + (-5)^2 = r^2

9 + 25 = r^2

r^2 = 34

5. Therefore, the equation of the circle is:
-

(x - 2)^2 + y^2 = 34

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Find the equation of the circle that has the center (2,0) and passes through (-1,-5)

Answer to a math question Find the equation of the circle that has the center (2,0) and passes through (-1,-5)

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