A parabola can be represented by the equation y squared is equal to negative x What are the coordinates of the focus and the equation of the directrix?
Answer
A
focus: open paren 1 fourth comma 0 close paren ; directrix: x is equal to negative 1 fourth
B
focus: open paren negative 4 comma 0 close paren ; directrix: x is equal to 4
C
focus: open paren 4 comma 0 close paren ; directrix: x is equal to negative 4
D
focus: open paren negative 1 fourth comma 0 close paren ; directrix: x is equal to 1 fourth
Explanation
Compare y² = −x with the standard form y² = 4px. Since 4p = −1, p = −1/4, so the focus is (−1/4, 0) and the directrix is x = −p = 1/4. This matches choice A.
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