Question

Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola? y = one fourthx2 + 3 y = −one fourthx2 + 3 y = −one fourthx2 − 3 y = one fourthx2 − 3

Answer 1

same as him took test right

Explanation:

Answer 2

y = -
`(1)/(4)` x² + 3

Explanation:

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

Using the distance formula

`√((x-0)^2+(y-2)^2)` = | y - 4 |, that is

`√(x^2+(y-2)^2)` = | y - 4 |

Squaring both sides

x² + (y - 2)² = (y - 4)² ← distribute parenthesis

x² + y² - 4y + 4 = y² - 8y + 16 ( subtract y² - 8y from both sides )

x² + 4y + 4 = 16 ( subtract x² + 4 from both sides )

4y = - x² + 12 ( divide both sides by 4 )

y = -
`(1)/(4)` x² + 3