Question

Find the equation of the parabola where the focus is at f(-1,3), passing through the point (3,6) and its axis of symmetry is parallel to the y-axis.

Answer 1

The equation of the parabola is x = (-1/12)y^2 + (1/4)y + 5/4.

Step-by-step explanation:

To find the equation of the parabola, we need to determine the values of a, b, and c in the general form of a parabola equation, which is ax^2 + bx + c.

Since the axis of symmetry is parallel to the y-axis, the equation of the parabola can be written as x = ay^2 + by + c.

Using the given focus point (-1,3), we can determine the value of a using the formula a = 1/(4p), where p is the distance from the vertex to the focus. In this case, p = 3.

Substituting the values of a and the coordinates of the focus into the equation, we can solve for b and c. Plugging in the coordinates of the point (3,6), we can solve for c.

Therefore, the equation of the parabola is x = (-1/12)y^2 + (1/4)y + 5/4.