Find the Expanded Form (x-5)^2+(y-6)^2=1

${(x - 5)}^{2} + {(y - 6)}^{2} = 1$

Step 1

Simplify the left side ${(x - 5)}^{2} + {(y - 6)}^{2}$ .

Simplify each term.

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$(x - 5) (x - 5) + {(y - 6)}^{2} = 1$

Expand $(x - 5) (x - 5)$ using the FOIL Method.

Apply the distributive property.

$x (x - 5) - 5 (x - 5) + {(y - 6)}^{2} = 1$

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 (x - 5) + {(y - 6)}^{2} = 1$

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5 + {(y - 6)}^{2} = 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5 + {(y - 6)}^{2} = 1$

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5 + {(y - 6)}^{2} = 1$

Multiply $- 5$ by $- 5$ .

$x^{2} - 5 x - 5 x + 25 + {(y - 6)}^{2} = 1$

Subtract $5 x$ from $- 5 x$ .

$x^{2} - 10 x + 25 + {(y - 6)}^{2} = 1$

Rewrite ${(y - 6)}^{2}$ as $(y - 6) (y - 6)$ .

$x^{2} - 10 x + 25 + (y - 6) (y - 6) = 1$

Expand $(y - 6) (y - 6)$ using the FOIL Method.

Apply the distributive property.

$x^{2} - 10 x + 25 + y (y - 6) - 6 (y - 6) = 1$

Apply the distributive property.

$x^{2} - 10 x + 25 + y \cdot y + y \cdot - 6 - 6 (y - 6) = 1$

Apply the distributive property.

$x^{2} - 10 x + 25 + y \cdot y + y \cdot - 6 - 6 y - 6 \cdot - 6 = 1$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 10 x + 25 + y^{2} + y \cdot - 6 - 6 y - 6 \cdot - 6 = 1$

Move $- 6$ to the left of $y$ .

$x^{2} - 10 x + 25 + y^{2} - 6 \cdot y - 6 y - 6 \cdot - 6 = 1$

Multiply $- 6$ by $- 6$ .

$x^{2} - 10 x + 25 + y^{2} - 6 y - 6 y + 36 = 1$

Subtract $6 y$ from $- 6 y$ .

$x^{2} - 10 x + 25 + y^{2} - 12 y + 36 = 1$

Simplify the expression.

Add $25$ and $36$ .

$x^{2} - 10 x + y^{2} - 12 y + 61 = 1$

Move $- 10 x$ .

$x^{2} + y^{2} - 10 x - 12 y + 61 = 1$

Step 2

Subtract $1$ from both sides of the equation.

$x^{2} + y^{2} - 10 x - 12 y + 61 - 1 = 0$

Step 3

Subtract $1$ from $61$ .

$x^{2} + y^{2} - 10 x - 12 y + 60 = 0$

Find the Expanded Form (x-5)^2+(y-6)^2=1

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