What is the equation of the parabola?
y = −one twelfthx2 − 2
y = one twelfthx2 − 2
y = −one twelfthx2 + 2
y = one twelfthx2 + 2

d

step-by-step explanation:

any point (x, y) on the parabola is equidistant from the focus and the directrix

here focus = (0, 5) and directrix is y = - 1

using the distance formula

= | y + 1 |

squaring both sides

x² + (y - 5)² = (y + 1)² ← expand parenthesis on both sides

x² + y² - 10y + 25 = y² + 2y + 1

subtract y² + 2y + 1 from both sides

x² - 12y + 24 = 0 ← subtract x² from both sides

- 12y + 24 = - x² ← subtract 24 from both sides

- 12y = - x² - 24 ( divide all terms by - 12 )

y = x² + 2 → d

-1/4 > -1 2/3. -1/4 is greater than -1 2/3 because it is closer to 0 on the number line.

  or  

sin y = 7/q

7 is the opposite side length, q is the hypotenuse

tan y = 7/r

7 is the opposite side length, r is the adjacent side length

using sohcahtoa ^^^^

cos y = adjacent/hypotenuse

cos y = r/q