Finding the Equation for a Hyperbola (10.3.2)

Question 1

• 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 1

• 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 2

• 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 2

• 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 3

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

Answer 3

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