Find the Symmetry x^2+2y^2-8x+8y+23=0

$x^{2} + 2 y^{2} - 8 x + 8 y + 23 = 0$

There are three types of symmetry:

1. X-Axis Symmetry

2. Y-Axis Symmetry

3. Origin Symmetry

If $(x, y)$ exists on the graph, then the graph is symmetric about the:

1. X-Axis if $(x, - y)$ exists on the graph

2. Y-Axis if $(- x, y)$ exists on the graph

3. Origin if $(- x, - y)$ exists on the graph

Check if the graph is symmetric about the x-axis by plugging in $- y$ for $y$ .

$x^{2} + 2 {(- y)}^{2} - 8 x + 8 (- y) + 23 = 0$

Simplify the left side.

Simplify each term.

Apply the product rule to $- y$ .

$x^{2} + 2 ({(- 1)}^{2} y^{2}) - 8 x + 8 (- y) + 23 = 0$

Raise $- 1$ to the power of $2$ .

$x^{2} + 2 (1 y^{2}) - 8 x + 8 (- y) + 23 = 0$

Multiply $y^{2}$ by $1$ .

$x^{2} + 2 y^{2} - 8 x + 8 (- y) + 23 = 0$

Multiply $- 1$ by $8$ .

$x^{2} + 2 y^{2} - 8 x - 8 y + 23 = 0$

Since the equation is not identical to the original equation, it is not symmetric to the x-axis.

Not symmetric to the x-axis

Check if the graph is symmetric about the y-axis by plugging in $- x$ for $x$ .

${(- x)}^{2} + 2 y^{2} - 8 (- x) + 8 y + 23 = 0$

Simplify the left side.

Simplify each term.

Apply the product rule to $- x$ .

${(- 1)}^{2} x^{2} + 2 y^{2} - 8 (- x) + 8 y + 23 = 0$

Raise $- 1$ to the power of $2$ .

$1 x^{2} + 2 y^{2} - 8 (- x) + 8 y + 23 = 0$

Multiply $x^{2}$ by $1$ .

$x^{2} + 2 y^{2} - 8 (- x) + 8 y + 23 = 0$

Multiply $- 1$ by $- 8$ .

$x^{2} + 2 y^{2} + 8 x + 8 y + 23 = 0$

Since the equation is not identical to the original equation, it is not symmetric to the y-axis.

Not symmetric to the y-axis

Check if the graph is symmetric about the origin by plugging in $- x$ for $x$ and $- y$ for $y$ .

${(- x)}^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23 = 0$

Solve for $- x^{2} - 2 y^{2} - 8 x + 8 y - 23$ .

Simplify the left side.

Simplify each term.

Apply the product rule to $- x$ .

${(- 1)}^{2} x^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23 = 0$

Raise $- 1$ to the power of $2$ .

$1 x^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23 = 0$

Multiply $x^{2}$ by $1$ .

$x^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23 = 0$

Apply the product rule to $- y$ .

$x^{2} + 2 ({(- 1)}^{2} y^{2}) - 8 (- x) + 8 (- y) + 23 = 0$

Raise $- 1$ to the power of $2$ .

$x^{2} + 2 (1 y^{2}) - 8 (- x) + 8 (- y) + 23 = 0$

Multiply $y^{2}$ by $1$ .

$x^{2} + 2 y^{2} - 8 (- x) + 8 (- y) + 23 = 0$

Multiply $- 1$ by $- 8$ .

$x^{2} + 2 y^{2} + 8 x + 8 (- y) + 23 = 0$

Multiply $- 1$ by $8$ .

$x^{2} + 2 y^{2} + 8 x - 8 y + 23 = 0$

Simplify the left side.

Simplify $- ({(- x)}^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23)$ .

Simplify each term.

Apply the product rule to $- x$ .

$- ({(- 1)}^{2} x^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23) = - (0)$

Raise $- 1$ to the power of $2$ .

$- (1 x^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23) = - (0)$

Multiply $x^{2}$ by $1$ .

$- (x^{2} + 2 {(- y)}^{2} - 8 (- x) + 8 (- y) + 23) = - (0)$

Apply the product rule to $- y$ .

$- (x^{2} + 2 ({(- 1)}^{2} y^{2}) - 8 (- x) + 8 (- y) + 23) = - (0)$

Raise $- 1$ to the power of $2$ .

$- (x^{2} + 2 (1 y^{2}) - 8 (- x) + 8 (- y) + 23) = - (0)$

Multiply $y^{2}$ by $1$ .

$- (x^{2} + 2 y^{2} - 8 (- x) + 8 (- y) + 23) = - (0)$

Multiply $- 1$ by $- 8$ .

$- (x^{2} + 2 y^{2} + 8 x + 8 (- y) + 23) = - (0)$

Multiply $- 1$ by $8$ .

$- (x^{2} + 2 y^{2} + 8 x - 8 y + 23) = - (0)$

Apply the distributive property.

$- x^{2} - (2 y^{2}) - (8 x) - (- 8 y) - 1 \cdot 23 = - (0)$

Simplify.

Multiply $2$ by $- 1$ .

$- x^{2} - 2 y^{2} - (8 x) - (- 8 y) - 1 \cdot 23 = - (0)$

Multiply $8$ by $- 1$ .

$- x^{2} - 2 y^{2} - 8 x - (- 8 y) - 1 \cdot 23 = - (0)$

Multiply $- 8$ by $- 1$ .

$- x^{2} - 2 y^{2} - 8 x + 8 y - 1 \cdot 23 = - (0)$

Multiply $- 1$ by $23$ .

$- x^{2} - 2 y^{2} - 8 x + 8 y - 23 = - (0)$

Simplify the right side.

Multiply $- 1$ by $0$ .

$- x^{2} - 2 y^{2} - 8 x + 8 y - 23 = 0$

Since the equation is not identical to the original equation, it is not symmetric to the origin.

Not symmetric to the origin

Determine the symmetry.

Not symmetric to the x-axis

Not symmetric to the y-axis

Not symmetric to the origin

Find the Symmetry x^2+2y^2-8x+8y+23=0

Related Questions

Support LCMGCF.com by disabling your adblocker.