What is the equation of a parabola with focus (-5, 3) and vertex (-5, 6)?

Solution:

Given that vertex of parabola = (h, k) = (-5, 6) and focus = (-5, 3)

Since the line joining the vertex and focus is an axis which is parallel to the y-axis, the equation of the parabola is of the form (x - h)² = 4a (y - k).

Also ‘a’ is the distance between vertex and focus.

The distance between vertex (-5, 6) and focus (-5, 3),

a = ❘y₂ - y₁❘

a = ❘3 - 6❘

a = 3

Therefore, the required equation is (x + 5)² = 12(y - 6).

What is the equation of a parabola with focus (-5, 3) and vertex (-5, 6)?

Summary:

The equation of a parabola with focus (-5, 3) and vertex (-5, 6) is (x + 5)² = 12(y - 6).