Respuesta :

standard form of a circle is (x-h)²+(y-k)²=r², (h, k) being the center, r the radius.
In this case, (x-h)²+(y-k)²=16
the circles pass through (1,1), that is x=1, y=1
Plug x=1,y=1 in the equation: (1-h)²+(1-k)²=16
if h=1, k is either -3 or 5
so the equation is (x-1)²+(y+3)²=16 or (x-1)²+(y-5)²=16

You can also set k=1, h=-3 or 5
Note: there are many other possibilities. 
abidemiokin

  • The first way of writing the equation of the circle is expressed as [tex](x-1)^2+(y-1)^2=16[/tex]
  • The second way of writing the equation of the circle is expressed as [tex]x^2+y^2-2x-2y-14=0[/tex]

The standard formula for finding the equation of a circle with centre (a, b) and radius "r" is expressed as:

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

Given the following parameters:

radius "r" = 4

centre (a, b) = (1, 1)

Substitute the given parameters into the formula as shown:

[tex](x-1)^2+(y-1)^2=4^2\\(x-1)^2+(y-1)^2=16[/tex]

This gives one way of expressing the equation of the line.

The other equation will be derived by expanding [tex](x-1)^2+(y-1)^2=16[/tex]

On expansion:

[tex](x-1)^2+(y-1)^2=16\\x^2-2x+1+y^2-2y+1=16\\x^2+y^2-2x-2y+1+1-16=0\\x^2+y^2-2x-2y-14=0[/tex]

Hene the second way of writing the equation of the circle is expressed as [tex]x^2+y^2-2x-2y-14=0[/tex]

Learn more here: https://brainly.com/question/22137754

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