Precalculus Examples

${(x - 5)}^{2} + {(y - 1)}^{2} = 25$ , $(8, - 3)$

Step 1

Insert the values of $x = 8$ and $y = - 3$ into the equation to find if the ordered pair is a solution.

${((8) - 5)}^{2} + {((- 3) - 1)}^{2} = 25$

Step 2

Simplify ${((8) - 5)}^{2} + {((- 3) - 1)}^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Subtract $5$ from $8$ .

$3^{2} + {((- 3) - 1)}^{2} = 25$

Step 2.1.2

Raise $3$ to the power of $2$ .

$9 + {((- 3) - 1)}^{2} = 25$

Step 2.1.3

Subtract $1$ from $- 3$ .

$9 + {(- 4)}^{2} = 25$

Step 2.1.4

Raise $- 4$ to the power of $2$ .

$9 + 16 = 25$

Step 2.2

Add $9$ and $16$ .

$25 = 25$

Step 3

Since $25 = 25$ , the equation will always be true.

Always true

Step 4

Since the equation is always true when the values are used, the ordered pair is a solution.

The ordered pair is a solution to the equation.