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Find the radius of the circle with equation x^2 - 4x + y^2 - 6y - 36 = 25

 Oct 16, 2021
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Hello,

 

(\({x}^{2}-4x+{y}^{2}-6y-36=25\)),

 

(\(x^2-4x-y^2-6y=25+36\)),

 

(\(x^2-4x+y^2-6y=61\)),

 

(\(x^2-4x+?+y^2-6y=61+?\)),

 

to solve the equation \(x^2-4x+4=(x-2)^2\),

 

we are adding 4:

 

(\(x^2-4x+4+y^2-6y=61+4\)),

 

factorise the expression using square of a binomial (\(a^2-2ab+b^2=(a-b)^2\)),

 

\((x-2)^2+y^2-6y=61+4\)

 

\((x-2)^2+y^2-6y=65\),

 

\((x-2)^2+y^2-6y+?=65+?\),

 

to solve the equation \(y^2-6y+9=(y-3)^2\),

 

we are adding 9:

 

\((x-2)^2+y^2-6y+9=65+9\),

 

factorise the expression using square of a binomial \(a^2-2ab+b^2=(a-b)^2\),

 

\((x-2)^2+(y-3)^2=65+9\),

 

\((x-2)^2+(y-3)^2=74\),

 

The equation can be written in the form \((x-p)^2+(y-q)^2=r^2\)

so that it corresponds to a circle with radius (\(r=\sqrt{74}\)) and centre (\(2,3\)).

 

Straight

 Oct 16, 2021

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