Answer:
Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)
Explanation:
* Lets revise some facts about the parabola
- Standard form equation for a parabola of vertex at (0 , 0)
- If the equation is in the form x² = 4py, then
- The axis of symmetry is the y-axis, x = 0
- 4p equal to the coefficient of y in the given equation to
solve for p
- If p > 0, the parabola opens up.
- If p < 0, the parabola opens down.
- Use p to find the coordinates of the focus, (0 , p)
- Use p to find equation of the directri , y= − p
- Use p to find the endpoints of the focal diameter, (±2p , p)
* Now lets solve the problem
- The vertex of the parabola is (0 , 0)
∵ -1/16x² = y ⇒ multiply each side by -16
∴ x² = -16y
∴ 4p = -16 ⇒ ÷ 4 tbe both sides
∴ p = -4
∵ The focus is (0 , p)
∴ The focus is (0 , -4)
∵ The directrix is y = -p
∴ The directrix is y = -(-4) = 4 ⇒ y = 4
∵ The endpoints of the focal diameter, (±2p , p)
∴ The focal width = 2p - (-2p) = 4p
∴ The focal width = 4 × I-4I = 16
* Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16