# What is the equation of the parabola that has a vertex at # (14, -9) # and passes through point # (0, -5) #?

##### 1 Answer

See explanation, for the existence of a family of parabolas

Upon imposing one more condition that that the axis is x-axis, we get a member

#### Explanation:

From definition of the parabola, the general equation to a parabola

having focus at

using 'distance from S = distance from DR'.

This equation has

As it passes through two points, we get two equations that relate

the

Of the two points, one is the vertex that bisects the perpendicular

from S to to DR,

one more relation. The bisection is implicit in the already obtained

equation. Thus, one parameter remains arbitrary. There is no unique

solution.

Assuming that the axis is x-axis, the equation has the form

So,

Perhaps, a particular solution like this is required.