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Type the correct answer in each box. A circle is centered at the point (5, -4) and passes through the point (-3, 2).


The equation of this circle is (x + )2 + (y + )2 =

Respuesta :

semsee45

Answer:

[tex](x-5)^2+(y+4)^2=100[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

  • (a, b) is the center
  • r is the radius

Given:

  • center = (5, -4)
  • point on circle = (-3, 2)

Substitute the given values into the circle equation and solve for r:

[tex]\implies r^2=(-3-5)^2+(2-(-4))^2[/tex]

[tex]\implies r^2=(-8)^2+(6)^2[/tex]

[tex]\implies r^2=64+36[/tex]

[tex]\implies r^2=100[/tex]

[tex]\implies r=\sqrt{100}[/tex]

[tex]\implies r=10[/tex]

Substitute the given center and the found value of r into the circle equation to create the equation of the circle:

[tex]\implies (x-5)^2+(y-(-4))^2=10^2[/tex]

[tex]\implies (x-5)^2+(y+4)^2=100[/tex]

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