Find the vertex, focus, directrix, and focal width of the parabola. (5 points) negative 1 divided by 16 times x squared = y

Step-by-step explanation:

Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)

Step-by-step 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

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.

segment bisector

step-by-step explanation:

line segment bisector. definition: a line, ray or segment which cuts another line segment into two equal parts. try this drag one of the orange dots at a or b and note the the line ab always divides the line pq into two equal parts.

mark brainliest!