Identifying a Conic (10.4.1)

Question 1

• You can determine whether an equation describes a conic section and which conic section an equation describes by completing the square for the x and y variables and factoring.

Answer 1

• You can determine whether an equation describes a conic section and which conic section an equation describes by completing the square for the x and y variables and factoring.

Question 2

• A parabola with vertex at (h, k) and focus at a distance of ±p from the vertex is described by the equation (x – h)^2 = 4p (y – k) or (y – k)^2 = 4p (x – h), depending on the direction that the parabola opens.

Answer 2

• A parabola with vertex at (h, k) and focus at a distance of ±p from the vertex is described by the equation (x – h)^2 = 4p (y – k) or (y – k)^2 = 4p (x – h), depending on the direction that the parabola opens.

Question 3

• The standard equation for an ellipse centered at the origin is x^2/a^2 + y^2/b^2=1, where the x-intercepts are at ±a and the y-intercepts are at ±b.
• The standard equation for an ellipse centered at (h,k) is (x-h)^2/a^2 + (y-k)^2/b^2=1.

Answer 3

• The standard equation for an ellipse centered at the origin is x^2/a^2 + y^2/b^2=1, where the x-intercepts are at ±a and the y-intercepts are at ±b.
• The standard equation for an ellipse centered at (h,k) is (x-h)^2/a^2 + (y-k)^2/b^2=1.

Question 4

• 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.
• 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 4

• 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.
• 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.