Graph x^2+y^2-10x+18y=-42

Solve Math

Trigonometry

$x^{2} + y^{2} - 10 x + 18 y = - 42$

Complete the square for $x^{2} - 10 x$ .

Tap for more steps...

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = - 10, c = 0$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = - \frac{10}{2 (1)}$

Simplify the right side.

Tap for more steps...

Cancel the common factor of $10$ and $2$ .

Tap for more steps...

Factor $2$ out of $10$ .

$d = - \frac{2 \cdot 5}{2 \cdot 1}$

Cancel the common factors.

Tap for more steps...

Factor $2$ out of $2 \cdot 1$ .

$d = - \frac{2 \cdot 5}{2 (1)}$

Cancel the common factor.

$d = - \frac{2 \cdot 5}{2 \cdot 1}$

Rewrite the expression.

$d = - \frac{5}{1}$

Divide $5$ by $1$ .

$d = - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$d = - 5$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Tap for more steps...

Simplify each term.

Tap for more steps...

Raise $- 10$ to the power of $2$ .

$e = 0 - \frac{100}{4 (1)}$

Multiply $4$ by $1$ .

$e = 0 - \frac{100}{4}$

Divide $100$ by $4$ .

$e = 0 - 1 \cdot 25$

Multiply $- 1$ by $25$ .

$e = 0 - 25$

Subtract $25$ from $0$ .

$e = - 25$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

${(x - 5)}^{2} - 25$

Substitute ${(x - 5)}^{2} - 25$ for $x^{2} - 10 x$ in the equation $x^{2} + y^{2} - 10 x + 18 y = - 42$ .

${(x - 5)}^{2} - 25 + y^{2} + 18 y = - 42$

Move $- 25$ to the right side of the equation by adding $25$ to both sides.

${(x - 5)}^{2} + y^{2} + 18 y = - 42 + 25$

Complete the square for $y^{2} + 18 y$ .

Tap for more steps...

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = 18, c = 0$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{18}{2 (1)}$

Cancel the common factor of $18$ and $2$ .

Tap for more steps...

Factor $2$ out of $18$ .

$d = \frac{2 \cdot 9}{2 \cdot 1}$

Cancel the common factors.

Tap for more steps...

Factor $2$ out of $2 \cdot 1$ .

$d = \frac{2 \cdot 9}{2 (1)}$

Cancel the common factor.

$d = \frac{2 \cdot 9}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{9}{1}$

Divide $9$ by $1$ .

$d = 9$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Tap for more steps...

Simplify each term.

Tap for more steps...

Raise $18$ to the power of $2$ .

$e = 0 - \frac{324}{4 (1)}$

Multiply $4$ by $1$ .

$e = 0 - \frac{324}{4}$

Divide $324$ by $4$ .

$e = 0 - 1 \cdot 81$

Multiply $- 1$ by $81$ .

$e = 0 - 81$

Subtract $81$ from $0$ .

$e = - 81$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

${(y + 9)}^{2} - 81$

Substitute ${(y + 9)}^{2} - 81$ for $y^{2} + 18 y$ in the equation $x^{2} + y^{2} - 10 x + 18 y = - 42$ .

${(x - 5)}^{2} + {(y + 9)}^{2} - 81 = - 42 + 25$

Move $- 81$ to the right side of the equation by adding $81$ to both sides.

${(x - 5)}^{2} + {(y + 9)}^{2} = - 42 + 25 + 81$

Simplify $- 42 + 25 + 81$ .

Tap for more steps...

Add $- 42$ and $25$ .

${(x - 5)}^{2} + {(y + 9)}^{2} = - 17 + 81$

Add $- 17$ and $81$ .

${(x - 5)}^{2} + {(y + 9)}^{2} = 64$

This is the form of a circle. Use this form to determine the center and radius of the circle.

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

Match the values in this circle to those of the standard form. The variable $r$ represents the radius of the circle, $h$ represents the x-offset from the origin, and $k$ represents the y-offset from origin.

$r = 8$

$h = 5$

$k = - 9$

The center of the circle is found at $(h, k)$ .

Center: $(5, - 9)$

These values represent the important values for graphing and analyzing a circle.

Center: $(5, - 9)$

Radius: $8$

Do you know how to Graph x^2+y^2-10x+18y=-42? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.