v=5i+j

Reorder 5i and x.

y=x+5i

Find the standard form of the hyperbola.

Subtract x from both sides of the equation.

y-x=5i

Divide each term by 5i to make the right side equal to one.

y5i-x5i=5i5i

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.

y5i-x5=1

y5i-x5=1

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

(x-h)2a2-(y-k)2b2=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=i5i

b=5

k=0

h=0

The asymptotes follow the form y=±b(x-h)a+k because this hyperbola opens left and right.

y=±i⋅x+0

Add i⋅x and 0.

y=ix

Add -i⋅x and 0.

y=-ix

This hyperbola has two asymptotes.

y=ix,y=-ix

The asymptotes are y=ix and y=-ix.

Asymptotes: y=ix,y=-ix

Asymptotes: y=ix,y=-ix

Graph v=5i+j