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NO LINKS! URGENT HELP PLEASE!

Write the equation of the following circles​

NO LINKS! URGENT HELP PLEASE! Write the equation of the following circles​-example-1
User RHPT
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1 Answer

7 votes

Answer:


\textsf{a)} \quad (x+1)^2+(y-4)^2=36


\textsf{b)} \quad (x-5)^2+(y+2)^2=64


\textsf{c)} \quad (x-3)^2+(y-7)^2=130

Explanation:

To write the equation of a circle given its center and radius, we can substitute the values into the standard circle equation formula.


\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}

Part a

Given values:

  • Center (a, b) = (-1, 4)
  • Radius r = 6

Substitute the values into the circle equation formula:


(x-(-1))^2+(y-4)^2=6^2

Therefore, the equation of the circle is:


\boxed{(x+1)^2+(y-4)^2=36}


\hrulefill

Part b

Given values:

  • Center (a, b) = (5, -2)
  • Diameter = 16

The diameter of a circle is twice its radius.

Therefore, if the diameter of the circle is 16, the radius is r = 8.

Substitute the values into the circle equation formula:


(x-5)^2+(y-(-2))^2=8^2

Therefore, the equation of the circle is:


\boxed{(x-5)^2+(y+2)^2=64}


\hrulefill

Part c

Given values:

  • Center (a, b) = (3, 7)
  • Point on the circle = (-4, -2)

Substitute the values into the circle equation formula and solve for r²:


(-4-3)^2+(-2-7)^2=r^2


(-7)^2+(-9)^2=r^2


49+81=r^2


r^2=130

Therefore, the equation of the circle is:


\boxed{(x-3)^2+(y-7)^2=130}

User Jack Dalton
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