Graph oi

$o i$

Find the standard form of the hyperbola.

Move all terms containing variables to the left side of the equation.

Subtract $x i$ from both sides of the equation.

$y - x i = 0$

Reorder $y$ and $- x i$ .

$- x i + y = 0$

Divide each term by $0$ to make the right side equal to one.

$- \frac{x i}{0} + \frac{y}{0} = \frac{0}{0}$

Simplify each term in the equation in order to set the right side equal to $1$ . The standard form of an ellipse or hyperbola requires the right side of the equation be $1$ .

$y - x i = 1$

This is the form of a hyperbola. Use this form to determine the values used to find the asymptotes of the hyperbola.

$\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$

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

$a = 1$

$b = 1$

$k = 0$

$h = 0$

The asymptotes follow the form $y = \pm \frac{b (x - h)}{a} + k$ because this hyperbola opens left and right.

$y = \pm 1 \cdot x + 0$

Simplify $1 \cdot x + 0$ .

Add $1 \cdot x$ and $0$ .

$y = 1 \cdot x$

Multiply $x$ by $1$ .

$y = x$

Simplify $- 1 \cdot x + 0$ .

Add $- 1 \cdot x$ and $0$ .

$y = - 1 \cdot x$

Rewrite $- 1 x$ as $- x$ .

$y = - x$

This hyperbola has two asymptotes.

$y = x, y = - x$

The asymptotes are $y = x$ and $y = - x$ .

Asymptotes: $y = x, y = - x$

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