An Introduction to Hyperbolas (10.3.1)

Question 1

• A hyperbola consists of the set of points, the difference of whose distances from two fixed points is a constant. The two fixed points are called the foci of the hyperbola. The singular form of foci is focus.

Answer 1

• A hyperbola consists of the set of points, the difference of whose distances from two fixed points is a constant. The two fixed points are called the foci of the hyperbola. The singular form of foci is focus.

Question 2

• The standard equation for a hyperbola centered at the origin that opens to the left and right is x^2/a^2-y^2/b^2=1, where the x-intercepts are at ±a . The foci of the hyperbola are located at (±c, 0), where c^2 = a^2 + b^2.

Answer 2

• The standard equation for a hyperbola centered at the origin that opens to the left and right is x^2/a^2-y^2/b^2=1, where the x-intercepts are at ±a . The foci of the hyperbola are located at (±c, 0), where c^2 = a^2 + b^2.

Question 3

• The standard equation for a hyperbola centered at the origin that open up and down is , where the y-intercepts are at ±b. The foci of the hyperbola are located at (0, ±c), where c^2 = a^2 + b^2.

Answer 3

• The standard equation for a hyperbola centered at the origin that open up and down is , where the y-intercepts are at ±b. The foci of the hyperbola are located at (0, ±c), where c^2 = a^2 + b^2.

Question 4

• In either case, the hyperbola has asymptotes along the lines y=±b/a x.

Answer 4

• In either case, the hyperbola has asymptotes along the lines y=±b/a x.

Question 5

• The transverse axis of a hyperbola passes through the foci.

Answer 5

• The transverse axis of a hyperbola passes through the foci.