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Murrr4er [49]
3 years ago
8

Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

Mathematics
1 answer:
Evgen [1.6K]3 years ago
7 0

The equation (x + 2)² + (y - 1)² = 25 represents a circle that contain the point (-5 , -3) and has a center at (-2 , 1)

Step-by-step explanation:

The equation of a circle of center (h , k) and radius r is:

(x - h)² + (y - k)² = r²

The given is:

  • The center of the circle is (-2 , 1)
  • The circle passes through point (-5 , -3)

The length of the radius is the distance from the center of the circle

to a point on the circle

∵ The formula of the distance is d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

∵ The center of the circle is (-2 , 1)

∵ The circle passes through point (-5 , -3)

∴ r=\sqrt{[(-5)-(-2)]^{2}+[(-3)-(1)]^{2}}

∴ r=\sqrt{[-3]^{2}+[-4]^{2}}

∴ r=\sqrt{9+16}

∴ r=\sqrt{25}

∴ r = 5

∵ The equation of the circle is (x - h)² + (y - k)² = r²

∵ The center of the circle is (-2 , 1)

∴ h = -2 and k = 1

∵ r = 5

∴ r² = (5)² = 25

- Substitute the values of h , k , r² in the equation of the circle

∴ (x - -2)² + (y - 1)² = 25

∴ (x + 2)² + (y - 1)² = 25

The equation (x + 2)² + (y - 1)² = 25 represents a circle that contains

the point (-5 , -3) and has a center at (-2 , 1)

Learn more:

You can learn more about the equation of the circle in brainly.com/question/9510228

LearnwithBrainly

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