SWBAT graph and write equations of hyperbolas in standard form. (Lesson 10 Section 9- 3)

Warm up:

1) A ___________________ is the set of all points (x,y) in a plane, the difference of whose distances from two distinct points, called _______________, is a positive constant.

2) The graph of a hyperbola has two disconnected parts called _____________________.

3) The line segment connecting the vertices of a hyperbola is called the _________________ ________________, and the midpoint of the line segment is the ____________________ of the hyperbola.

4) Each hyperbola has two _____________ that intersect at the center of the hyperbola.


SWBAT graph and write equations of hyperbolas in standard form. (Lesson 10 Section 9- 3)


SWBAT graph and write equations of hyperbolas in standard form. (Lesson 10 Section 9- 3)

Example 1) Find an equation for the hyperbola with center at

(–1, 3), one focus at (– 1, – 1), and one vertex at (– 1, 4). Graph the equation by hand.


SWBAT graph and write equations of hyperbolas in standard form. (Lesson 10 Section 9- 3)

Example 2)


Example 3) Classify the graph of each equation

The equation of every conic can be written in the following form:

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.

Assuming a conic is not degenerate, the following conditions hold true: If

· AC > 0, the conic is an ellipse or a circle

· AC < 0, the conic is a hyperbola

· AC = 0, and A and C are not both zero, the conic is a parabola

· A = C, the conic is a circle.

a)

b)

c)

d)