Answer:
[tex] {x}^{2} + {y}^{2} - 14x - 2x + 50 = 25[/tex]
Step-by-step explanation:
To put this expression in general form, distribute, combine the like terms, further simplify, and give the answer.
Let us start solving by:
(1) Distributing
[tex] {(x - 7)}^{2} + {(y - 1)}^{2} = 25 \\ {x}^{2} + - 14x + 49 + {y}^{2} + - 2y + 1 = 25[/tex]
(2) Combining the like terms
[tex] {x}^{2} + - 14x + 49 + {y}^{2} + - 2y + 1 = 25 \\ ( {x}^{2} ) + ( - 14x )+ (49 + 1 )+ ({y}^{2} ) + ( - 2y) = 25 \\ {x}^{2} + - 14x + 50 + {y}^{2} + - 2y = 25[/tex]
(3) Further simplifying
(3a) Putting the order
[tex] {x}^{2} + - 14x + 50 + {y}^{2} + - 2y = 25 \\ {x}^{2} + {y}^{2} + - 14x + - 2y + 50 = 25[/tex]
(3b) Putting the opposites as a negative
[tex] {x}^{2} + {y}^{2} + - 14x + - 2y + 50 = 25 \\ {x}^{2} + {y}^{2} - 14x - 2y + 50 = 25[/tex]
(4) Giving the answer
The general form of [tex] {(x - 7)}^{2} + {(y - 1)}^{2} = 25[/tex] is [tex] {x}^{2} + {y}^{2} - 14x - 2y + 50 = 25[/tex].
