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In the standard equations (x - h)2 / a2 - (y - k)2 / b2 = 1 and -(x - h)2 / a2 + (y - k)2 / b2 = 1 the point (h, k) represents the centre of the hyperbola.

What do the values of a and b tell us about the graph of a hyperbola?

Previously, you saw that a and b effect the slopes of the asymptotes and the location of the vertices in standard equations of hyperbolas centred at the origin.

Use the following action figure and question box to explore what effect a and b have on the graph of hyperbolas centred at (h, k).

You will again be asked to use the two buttons at the bottom left corner of the action figure which allow you to switch between hyperbolas that open right and left (x2 - y2 = 1) and hyperbolas that open up and down (-x2 + y2 = 1).

	(x - h)2	-	(y - k)2	= 1	or	-	(x - h)2	+	(y - k)2	= 1
	a2		b2				a2		b2