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 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 [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
∵ The center of the circle is (-2 , 1)
∵ The circle passes through point (-5 , -3)
∴ [tex]r=\sqrt{[(-5)-(-2)]^{2}+[(-3)-(1)]^{2}}[/tex]
∴ [tex]r=\sqrt{[-3]^{2}+[-4]^{2}}[/tex]
∴ [tex]r=\sqrt{9+16}[/tex]
∴ [tex]r=\sqrt{25}[/tex]
∴ 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
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