Question

Equation of parabola having focii (-3, 1) and (3, 1)

• A. \( y^2 = 4x \)
• B. \( x^2 = 4y \)
• C. \( x^2 = 4y - 1 \)
• D. \( y^2 = 4(x + 3)(x - 3) \)

Hint:

For parabolas, the focus and directrix are key to determining the equation. The vertex is at the midpoint between the foci, and the distance between the vertex and the focus is denoted as \( p \).

Answer 1

The Correct Option is D

The general equation of a parabola with its focus at \( (h, k) \) is given by: \[ (y - k)^2 = 4p(x - h) \] However, the equation of the parabola with focii at \( (-3, 1) \) and \( (3, 1) \) indicates that the vertex of the parabola is at the midpoint of the foci. The midpoint of the foci is \( (0, 1) \). The equation of the parabola can thus be written as: \[ y^2 = 4(x + 3)(x - 3) \] This equation satisfies the given conditions. Therefore, the correct equation of the parabola is (D).