Precalculus Examples

$x^{2} + {(y - 5)}^{2} = 12$

Step 1

Simplify each term.

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Step 1.1

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

$x^{2} + (y - 5) (y - 5) = 12$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$x^{2} + y (y - 5) - 5 (y - 5) = 12$

Step 1.2.2

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 5 - 5 (y - 5) = 12$

Step 1.2.3

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 5 - 5 y - 5 \cdot - 5 = 12$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $y$ by $y$ .

$x^{2} + y^{2} + y \cdot - 5 - 5 y - 5 \cdot - 5 = 12$

Step 1.3.1.2

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

$x^{2} + y^{2} - 5 \cdot y - 5 y - 5 \cdot - 5 = 12$

Step 1.3.1.3

Multiply $- 5$ by $- 5$ .

$x^{2} + y^{2} - 5 y - 5 y + 25 = 12$

Step 1.3.2

Subtract $5 y$ from $- 5 y$ .

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

Step 2

Subtract $12$ from both sides of the equation.

$x^{2} + y^{2} - 10 y + 25 - 12 = 0$

Step 3

Subtract $12$ from $25$ .

$x^{2} + y^{2} - 10 y + 13 = 0$