Calculus- Early Transcendentals, 2021a

1.2. Analytic Geometry 27
• b is the vertical distance from the centre to the edge of the ellipse.
Horizontal Hyperbola: The equation of a horizontal hyperbola is:
• (h,k) is the centre of the hyperbola.
(x − h) 2 (y − k)2
a 2 −
b 2 = 1
• a is the horizontal distance from the centre to
the edge of the box.
• a,b are the reference box values. The box has
a centre of (h,k).
• b is the vertical distance from the centre to the
edge of the box.
Given the equation of a horizontal hyperbola, one may sketch it by first placing a dot at the point (h,k).
Then draw a box around (h,k) with horizontal distance a and vertical distance b to the edge of the box.
Then draw dotted lines (called the asymptotes of the hyperbola) through the corners of the box. Finally,
sketch the hyperbola in a horizontal direction as illustrated below.
Vertical Hyperbola: The equation of a vertical hyperbola is:
• (h,k) is the centre of the hyperbola.
(x − h) 2 (y − k)2
a 2 −
b 2 = −1
• a is the horizontal distance from the centre to
the edge of the box.
• a,b are the reference box values. The box has
a centre of (h,k).
• b is the vertical distance from the centre to the
edge of the box.
Given the equation of a vertical hyperbola, one may sketch it by following the same steps as with a
horizontal hyperbola, but sketching the hyperbola going in a vertical direction.