Answer:
[tex]x^2+y^2-8x-4y+11=0[/tex]
Step-by-step explanation:
We want to find the equation of the circle: [tex](x-4)^2+(y-2)^2=9[/tex] in general form.
We need to expand the parenthesis to obtain: [tex]x^2-8x+16+y^2-4y+4=9[/tex]
This implies that:
[tex]x^2+y^2-8x-4y+20=9[/tex]
We add -9 to both sides of the equattion to get:
[tex]x^2+y^2-8x-4y+20-9=0[/tex]
Simplify the constant terms to get:
[tex]x^2+y^2-8x-4y+11=0[/tex]
The general form of the equation is x^2 + y^2 - 8x -4y - 11 = 0
The equation is given as:
(x-4)^2+(y-2)^2=9
Evaluate the exponents
x^2 - 8x + 16 + y^2 -4y + 4 = 9
Collect like terms
x^2 - 8x + y^2 -4y - 9 + 16 + 4 = 0
Evaluate the like terms
x^2 - 8x + y^2 -4y - 11 = 0
Rewrite as:
x^2 + y^2 - 8x -4y - 11 = 0
Hence, the general form of the equation is x^2 + y^2 - 8x -4y - 11 = 0
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