Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

# What do a and b represent in the equation of a hyperbola?

In the general equation of a hyperbola color(white)("XXX")a  represents the distance from the vertex to the center color(white)("XXX")b  represents the distance perpendicular to the transverse axis from the vertex to the asymptote line(s).

For a hyperbola with a horizontal transverse axis, the general formula is: color(white)("XXX")(x^2)/(a^2)-(y^2)/(b^2)=1

For a hyperbola with a vertical transverse axis, the general formula is: color(white)("XXX")(y^2)/(a^2)-(x^2)/(b^2)=1

Note that the (a^2) always goes with the positive of x^2 or y^2

The significance of a and b can (hopefully) be seen by the diagrams below: (the color(red)("red lines") represent the and are not part of the hyperbolae)

For a hyperbola with a horizontal transverse axis, the slopes of the two asymptotes are b/a and -(b/a)

For a hyperbola with a vertical transverse axis the slopes of the two asymptotes are a/b and -a/b

{I hope the reason for this is clear from the above diagrams and the definition of slope.]