Find the equation of the parabola whose vertex is O(0, 0) and focus at

1.	Find the equation of the parabola whose vertex is O(0, 0) and focus at (-7, 0).
Answer» Focus of the parabola is S(-7, 0) and vertex is O(0, 0). Since focus lies on X-axis, it is the axis of the parabola. Focus S(-7, 0) lies on the left-hand side of the origin. It is a left-handed parabola. Required parabola is y = -4ax. Focus is S(-a, 0). a = 7 ∴ The required equation of the parabola is y² =-4(7)x, i.e., y² = -28x.

Find the equation of the parabola whose vertex is O(0, 0) and focus at (-7, 0).

Answer»

Focus of the parabola is S(-7, 0) and vertex is O(0, 0).

Since focus lies on X-axis, it is the axis of the parabola.

Focus S(-7, 0) lies on the left-hand side of the origin.

It is a left-handed parabola. Required parabola is y = -4ax.

Focus is S(-a, 0). a = 7

∴ The required equation of the parabola is y²

=-4(7)x, i.e., y² = -28x.